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First published December, 2010
Printed in India
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Ferroelectrics, Edited by Indrani Coondoo
p. cm.
ISBN 978-953-307-439-9
free online editions of InTech
Books and Journals can be found at
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Part 1
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Preface IX
Ferroelectrics and Its Application: Bulk and Thin Films 1
Principle Operation of 3–D Memory Device
based on Piezoacousto Properties of Ferroelectric Films 3
Ju. H. Krieger
Ferroelectric and Multiferroic Tunnel Junctions 17
Tianyi Cai, Sheng Ju, Jian Wang and Zhen-Ya Li
Photoluminescence in Low-dimensional
Oxide Ferroelectric Materials 43
Dinghua Bao
Optical Properties and Electronic Band
Structures of Perovskite-Type Ferroelectric
and Conductive Metallic Oxide Films 63
Zhigao Hu, Yawei Li, Wenwu Li, Jiajun Zhu,
Min Zhu, Ziqiang Zhu and Junhao Chu
Epitaxial SrRuO
3
Thin Films Deposited
on SrO buffered-Si(001) Substrates
for Ferroelectric Pb(Zr
0.2
Ti
0.8
)O
3
Thin Films 89
Soon-Gil Yoon
Electrocaloric Effect (ECE) in Ferroelectric Polymer Films 99
S. G. Lu, B. Rožič, Z. Kutnjak and Q. M. Zhang
Study on Substitution Effect
of Bi
4
Ti
3
O
12
Ferroelectric Thin Films 119
Jianjun Li, Ping Li and Jun Yu
Uniaxially Aligned Poly(p-phenylene vinylene)
and Carbon Nanofiber Yarns through
Electrospinning of a Precursor 139
Hidenori Okuzaki and Hu Yan
Contents
Contents VI
Applications of Carbon Materials
for Ferroelectric and Related Materials 155
Young-Seak Lee, Euigyung Jeong and Ji Sun Im
Dielectric Relaxation Phenomenon
in Ferroelectric Perovskite-related Structures 165
A. Peláiz-Barranco and J. D. S. Guerra
The Ferroelectric-Ferromagnetic Composite
Ceramics with High Permittivity
and High Permeability in Hyper-Frequency 187
Yang Bai
Aging-Induced, Defect-Mediated Double
Ferroelectric Hysteresis Loops and Large
Recoverable Electrostrain Curves in Mn-Doped
Orthorhombic KNbO
3
-Based Lead-Free Ceramics 207
Siu Wing Or
Effects of B-site Donor and Acceptor Doping
in Pb-free (Bi
0.5
Na
0.5
)TiO
3
Ceramics 217
Yeon Soo Sung and Myong Ho Kim
Enhanced Dielectric and Ferroelectric Properties of Donor
(W
6
+
, Eu
3
+
) Substituted SBT Ferroelectric Ceramics 231
Indrani Coondoo and Neeraj Panwar
Ferroelectrics and Its Applications:
A Theoretical Approach 251
Non-Equilibrium Thermodynamics
of Ferroelectric Phase Transitions 253
Shu-Tao Ai
Theories and Methods of First Order
Ferroelectric Phase Transitions 275
C L Wang
Electroacoustic Waves in a Ferroelectric Crystal
with of a Moving System of Domain Walls 301
Vilkov E.A. and Maryshev S.N.
Ferroelectric Optics: Optical Bistability
in Nonlinear Kerr Ferroelectric Materials 335
Abdel-Baset M. A. Ibrahim, Mohd Kamil Abd Rahman,
and Junaidah Osman
Chapter 9
Chapter 10
Chapter 11
Chapter 12
Chapter 13
Chapter 14
Part 2
Chapter 15
Chapter 16
Chapter 17
Chapter 18
Contents VII
Nonlinear Conversion Enhancement for
Efficient Piezoelectric Electrical Generators 357
Daniel Guyomar and Mickaël Lallart
Quantum Chemical Investigations of Structural Parameters
of PVDF-based Organic Ferroelectric Materials 381
A. Cuán, E. Ortiz, L. Noreña, C. M. Cortés-Romero, and Q. Wang
An Exact Impedance Control
of DC Motors Using Casimir Function 399
Satoru Sakai
Stabilization of Networked Control Systems
with Input Saturation 405
Sung Hyun Kim and PooGyeon Park
Robust Sampled-Data Control Design of Uncertain
Fuzzy Systems with Discrete and Distributed Delays 417
Jun Yoneyama, Yuzu Uchida and Makoto Nishigaki
Numerical Solution of a System
of Polynomial Parametric form Fuzzy Linear Equations 433
Majid Amirfakhrian
Chapter 19
Chapter 20
Chapter 21
Chapter 22
Chapter 23
Chapter 24
Preface
This book reviews a wide range of diverse topics related to the phenomenon of fer-
roelectricity (in the bulk as well as thin ﬁlm form) and provides a forum for scientists,
engineers, and students working in this ﬁeld. It contains records of original research
that provide or lead to fundamental principles in the science of ferroelectric materials.
The present book is a result of contributions of experts from international scientiﬁc
community working in diﬀerent aspects of ferroelectricity related to experimental and
theoretical work aimed at the understanding of ferroelectricity and their utilization in
devices. It provides an up-to-date insightful coverage to the synthesis, characteriza-
tion, functional properties and potential device applications in specialized areas. The
readers will perceive a trend analysis and examine recent developments in diﬀerent
ﬁelds of applications of ferroelectric materials. Based on the thematic topics, it contains
the following chapters:
Chapter 1 gives a detailed description of new operation principle of memory devices
based on piezoacousto properties of ferroelectric ﬁlms – the Acousto-FeRAM (AFeR-
AMs). It is based on the two physical properties of a ferroelectric ﬁlm (two-in-one), the
intrinsic memory phenomenon for information storage and piezoacousto property for
eﬀective read-out info. It allows the design and implementation of 3-D memory devices
with universal characteristics of the inherent ferroelectric memory.
Chapter 2 deals with the studies on the tunneling eﬀect and the magnetoelectric cou-
pling in ferroelectric-based junctions. This chapter suggests connecting conventional
electronics with spintronics at the nanoscale and several low-power approaches for
spin-based information control.
Chapter 3 reports the observance of photoluminescence in low-dimensional oxide fer-
roelectric materials in lanthanide-doped Bi
4
Ti
3
O
12
thin ﬁlms. Co-doping of rare earth
ions such as Eu/Gd, Pr/La, Er/Yb in bismuth titanate thin ﬁlms is found to be an eﬀec-
tive way to improve photoluminescence and electrical properties of the thin ﬁlms.
Chapter 4 examines the optical properties and electronic band structures of perovskite-
type ferroelectric and conductive metallic oxide ﬁlms. Temperature inﬂuence on the
optical properties of the BLT ﬁlm prepared by chemical solution method on quartz
substrate has been studied by the transmitance measurements. The Adachi’s model
X Preface
has been employed to calculate the dielectric functions of high-quality LNO and LSCO
conductive oxide ﬁlms.
Chapter 5 reports on SrRuO
3
botom electrodes grown with an epitaxial relationship
with SrO buﬀered-Si(001) substrates by pulsed laser deposition. The structural and
electrical properties of the SrRuO
3
ﬁlms have been studied with deposition param-
eters of SrRuO
3
on the optimized SrO buﬀer layered Si (001) substrates. 100nm thick-
Pb(Zr
0.2
Ti
0.8
)O
3
thin ﬁlms deposited at 575
o
C on SrRuO
3
/SrO/Si substrates showed a (00l)
preferred orientation and exhibited a 2P
r
of 40 μC/cm
2
and a E
c
of 100 kV/cm.
In Chapter 6 the experimental results on Electro Caloric Eﬀect (ECE) in ferroelectric
polymer ﬁlms. The relaxor ferroelectric P(VDF-TrFE-CFE) terpolymer has been stud-
ied which reveal a very large ECE at ambient condition in the relaxor terpolymers.
Chapter 7 studies the subtitutional eﬀect in Bi
4
Ti
3
O
12
ferroelectric thin ﬁlms. BIT, BLT,
BTV and BLTV thin ﬁlms were fabricated on the Pt/TiO
2
/SiO
2
/p-Si(100) substrates by
sol-gel processes. The BLTV thin ﬁlm shows the largest 2P
r
of 50.8 μC/cm
2
with small
2E
c
of 194 kV/cm among these ﬁlms. For the BLTV thin ﬁlm, the fatigue test showed the
strongest fatigue endurance up to 10
10
cycles with leakage current density in the order
of 10
-9
-10
-8
A/cm
2
.
Chapter 8 reports the successful fabrication of uniaxially aligned semiconducting,
conducting, and carbon nanoﬁber yarns by electrospinning and subsequent thermal
conversion or carbonization of PXTC, which would open up a new ﬁeld of applications
in organic nanoelectronics.
Chapter 9 reports on the introduction of carbon materials where in the excellent elec-
trical properties of carbon materials enable them to assist the applications of ferroelec-
tric and related materials.
In Chapter 10, the dielectric relaxation phenomenon is discussed in ferroelectric per-
ovskite-related structures considering the relaxation mechanisms and the inﬂuence of
the vacancies on them.
Chapter 11 reports on the ferroelectric-ferromagnetic composite ceramics with high
permitivity and high permeability in hyper-frequency. The co-ﬁred composite ceram-
ics of 0.8Pb(Ni
1/3
Nb
2/3
)O
3
-0.2PbTiO
3
/Ba
2
Zn
1.2
Cu
0.8
Fe
12
O
22
are discussed in this chapter,
which has excellent co-ﬁring behavior, dense microstructure and good electromag-
netic properties.
Chapter 12 investigates the aging-induced double ferroelectric hysteresis (P–E) loops
and recoverable electrostrain (S–E) curves in an Mn-doped orthorhombic KNbO
3
-
based [K(Nb
0.90
Ta
0.10
)O
3
] lead-free ceramic: K[(Nb
0.90
Ta
0.10
)
0.99
Mn
0.01
]O
3
. Double P–E loops
and large recoverable S–E curves with amplitudes in excess of 0.13% at 5 kV/mm have
been observed in the aged samples over a wide temperature range of 25–140
o
C.
XI Preface
Chapter 13 deals with the co-relation between piezoelectric properties and grain size
aﬀected by defects in Nb
5+
and Mn
3+
doping in Pb-free (Bi
0.5
Na
0.5
)(Ti
1-x
D
x
)O
3
(D = Nb or
Mn) ceramics.
Chapter 14 shows enhanced dielectric and ferroelectric properties of donor (W
6+
, Eu
3+
)
substituted SrBi
2
Ta
2
O
9
ferroelectric ceramics. Also, W and Eu doping in SBT results in
reduced dielectric loss and conductivity.
Chapter 15 talks about non-equilibrium thermodynamics of ferroelectric phase transi-
tions. The authors provide both experimental and theoretical evidence for the existence
of stationary states to a ferroelectric phase transition. Moreover they have given the
non-equilibrium (irreversible) thermodynamic description of phase transitions and ex-
planation of the irreversibility of ferroelectric phase transitions.
Chapter 16 gives a detailed description of the theories and methods of ﬁrst order fer-
roelectric phase transitions Heavy-computer relying methods, such as ﬁrst-principle
calculations and molecular dynamic simulations etc, have been applied to investigate
the physical properties of ferroelectrics.
Chapter 17 deals with electroacoustic waves in a ferroelectric crystal with moving do-
main walls (DW). The eﬀect of the uniform motion of ferroelectric DWs that form a
dynamic superlatice on the spectral properties of EWs has been analyzed for the ﬁrst
time. It is put forth that the velocity of domain-wall motion serves as a new parameter
that is convenient for controlling the reﬂection and transmission of waves in combi-
nation with their frequency shifs and this induced acoustic nonreciprocity and the
Doppler frequency conversion can be used for the development of sensors and acousto-
electronic devices for data conversion with the frequency output.
Chapter 18 deals with an theoretical approach to ferroelectric Optics: Optical Bistabil-
ity in Nonlinear Kerr Ferroelectric Materials wherein the Maxwell-Duﬃ ng analysis
has been employed to study the optical bistability of a ferroelectric slab as well as a
Fabry-Perot resonator coated with two identical partially-reﬂecting dielectric mirrors.

Chapter 19 exposes the use of nonlinear treatments for energy harvesting enhance-
ment. It has been demonstrated that the conversion enhancement by application of
switching approach (allowing both a voltage increase and a reduction of the time shif
between voltage and velocity), concept to energy harvesting (SSHI) allows a signiﬁcant
gain in terms of harvested power (7-8 times greater than the standard interface) or
signiﬁcantly reduce the amount of piezoelectric material required to harvest a given
amount of energy.
Chapter 20 deals with quantum chemical investigations of the energetics and struc-
tures corresponding to the diﬀerent structural conformations for the PVDF, P(VDF-
TrFE) and P(VDF-CTFE) units.
XII Preface
Chapter 21 provides a solution for an exact impedance control for electro-mechanical
systems. The authors give a new model of DC motor with dynamics between the torque
and control input. They propose a new impedance control which is based on Casimir
function.
In Chapter 22 the problem of designing an H
∞
control for networked control systems
(NCSs) with the eﬀects of both the input saturation as well as the network-induced
delay have been addressed.
In Chapter 23, robust sampled-data control and observer design for uncertain fuzzy
systems with discrete, neutral and distributed delays has been considered. A controller
design method has been proposed via LMI conditions.
Chapter 24 proposes a new method of numerical solution to solve a system of linear
equations. The presented method can be applied on any system of equations with LR
fuzzy number coeﬃ cients.
We hope that this book will prove to be timely and thought provoking and will serve as
a valuable reference for researchers working in diﬀerent areas of ferroelectric materi-
als. Special thanks go to the authors for their valuable contributions.
Indrani Coondoo
Departamento de Engenharia Cerâmica e do Vidro (DECV) & CICECO
Universidade de Aveiro, 3810-193 Aveiro,
Portugal
Part 1
Ferroelectrics and Its Application:
Bulk and Thin Films
1
Principle Operation of 3–D Memory Device
based on Piezoacousto Properties of
Ferroelectric Films
Ju. H. Krieger
Academgorodoc
Russia
1. Introduction
At present, the main driving forces for rapidly growing the market of nonvolatile memory
devices and nonvolatile memory technology are portable electronics. Technical innovations
will continue to drive the increase of memory density and speed in the future. For
traditional nonvolatile memory devices like NOR flash, scaling could stop even before the
32nm node, while scaling of mass storage devices like NAND flash, is going to be very
difficult beyond the 20nm node, too.
In recent years, more research efforts have been devoted to finding a new memory
technology able to overcome performance and scalability limits of currently memory
devices. However as lithographic scaling becomes more challenging. Novel architectures are
needed to improve memory device performances in embedded as well as stand-alone
memory applications. It is now generally recognized that 3–D integration and vertically
stacking are possible alternatives to scaling. In order to realize stacked memory cells a novel
physical principle operation of a memory element is needed.
Many new ideas have been proposed to find out the solution of such problems. Recently, it
were developed a rewriteable 3–D NAND flash memory chip called Bit Cost Memory (BiCS)
in which it stacked memory arrays vertically (Fukuzumi & et al., 2007) and 3–D double-
stacked multi-level NAND flash memory (Park & et al., 2009). However, there is a cross talk
between neighbouring memory cells in the same plane and between vertical neighbours in
adjacent planes, too. It is a new challenge in addition to scaling issues. The major limitation,
however, is likely to be power dissipation where 3–D designs are not efficient at dissipating
heat. More over 3–D architectures are required to overcome a tyranny of interconnects.
From physical point of view, a memory device based on ferroelectric phenomena is more
suitable for creating 3–D architectures of universal memory devices. Ferroelectric materials
can be electrically polarized in certain direction. Then, the polarization is retained after the
polarizing field is removed. Therefore, these materials have intrinsic memory. Ferroelectric
random access memory (FeRAM) is widely considered as an ideal nonvolatile memory with
high write speeds, low-power operation and high endurance (Scott, 2000; Pinnow &
Mikolajick, 2004). FeRAM also have an added significant advantage, which is high radiation
hardness. FeRAM are inherently radiation-hard making it very suitable for space
applications. The FeRAM with lowest active power is a voltage-controlled device as
Ferroelectrics

4
opposed to a magnetic, a phase change and a switchable resistor type of memory, which are
current-controlled devices with high power consumption. In scaled memory device, current-
driven devices have not survived. There is needed a low resistance material for a nanoscale
signal-line.
In order to realize all good performance of ferroelectric memory devices and to simplify a
problem of creating 3–D memory devices a novel physical principle of memory device
operations are needed. The one of the advantages a physical principle of ferroelectric
memory device operation is Acousto-Ferroelectric Memory Device (AFeRAM) has been
published recently (Krieger, 2008, 2009). The new universal memory device is called
Acousto-Ferroelectric RAM (AFeRAM) makes use of acoustic method of detecting the
direction of the spontaneous polarization of the ferroelectric memory cells. The physical
principle of AFeRAM device operations is based on a polarization dependent of an acoustic
response from a ferroelectric memory cell under the action of applied electrical field pulse.
In this chapter, it will be presents physical principle, 3–D architectures and operation modes
of the new type of universal memory devices based on piezoacusto properties of
ferroelectric materials.
2. Ferroelectric random access memory (FeRAM)
Ferroelectric Random Access Memory (FeRAM) has been studied for over fifty years. The
FeRAM devices are divided into two categories based on the readout technique: destructive
read-out (DRO) FeRAM and non-destructive read-out (NDRO) FeRAM (Scott, 2000). The
first one is capacitor-type, where ferroelectric capacitors are used to store the data and
FeRAM with 1T/1C (or 2T/2C, etc.) configurations. This structure is composed of a
ferroelectric capacitor (C) to store data and a transistor (T) to access it similar to a DRAM
cell. The read operation is based on reading current, which results from changes in
polarization when voltage is applied to the cell. Accordingly, the data stored in the cell are
destroyed in each read cycle. In other words, the read operation is destructive. Therefore,
the data needs to be re-written in each cycle. Another main issue of FeRAM memories with
1T/1C or 2T/2C configuration is that it cannot be easily scaled down. The absolute value of
the ferroelectric polarization is important for capacitor-type FeRAM. It is necessary to look
for new ferroelectric materials with the high intrinsic remanent polarization and using high
program voltage. At the same time, ferroelectric memory cells based on ferroelectric
materials with the high remanent polarization are usually characterised by low endurance
as a consequence of fatigue phenomena in ferroelectric films. Moreover this FeRAM device
based on ferroelectric materials with a high remanent polarization, as a rule, have bad
endurance and fatigue property, which don’t allow to use this type of FeRAM as DRAM
device. Therefore, many companies have suspended development of this type of memory.
The second type of memory is transistor-type (like Flash), in which ferroelectric-gate field
effect transistors (FeFET-type) are used to store the data (Miller, 1992; Scott, 2000).
Ferroelectric-gate field effect transistors, in which the gate insulator film is composed of a
ferroelectric material, have attracted much attention because the ferroelectric gate area can
be scaled down in proportion to the FeFET size. Thus, FeFET has high potential for use in
large-scale FeRAM with 1 Gigabit or higher density. In other words, charge density (charge
per unit area) of the ferroelectric polarization is an important parameter to achieve non-
volatility in transistor-type FeRAM, whereas the absolute value of the ferroelectric
polarization is important for capacitor-type FeRAM.
Principle Operation of 3–D Memory Device
based on Piezoacousto Properties of Ferroelectric Films

5
Typical values of remanent polarization for the ferroelectric gate material are extremely
different from those for FeRAM with 1T/1C configuration. The latter require remanent
polarization of 20–40 µC/cm
2
, whereas the ferroelectric-gated FeFETs can function well with
100-200 times lower remanent polarization (0.1–0.2 µC/cm
2
) (Miller, 1992; Dawber, 2005).
However, FeFET memory devices generally have short data retention times due to leakage,
depolarization, or both.
Another main issue of FeFET memory is high program voltage. In order to prevent the
chemical reaction between the Si substrate and the ferroelectric film, an insulator buffer
layer must be inserted between them. For this reason, the program voltage becomes large
due to voltage drop on the buffer layer between Si and ferroelectric films. Nonetheless, the
FeFET type memory continues to attract much interest. It is well recognized that only non-
destructive read-out (NDRO) of ferroelectric memory cells should realize all good
performance of ferroelectric memory devices. By the way another important feature of
FeFET is its high sensitivity to intrinsic remanent polarization of the ferroelectric gate that
can be used for detecting mechanical stress or acoustic waves (Greeneich & Muller, 1972;
Greeneich & Muller, 1975). At the same time, the information about ferroelectric gate
polarization is not lost and can be extracted by heating (pyroelectric approach) or
mechanical deformation (piezoacousto approach) of ferroelectric memory cell (Krieger,
2009).
Ferroelectric materials display a number of physical phenomena (pyroelectricity,
piezoelectricity), which allow us to obtain information about the intrinsic remanent
polarization by generating additional charge in the ferroelectric film, which is proportional
to the value and polarity of the intrinsic remanent polarization. In general, all ferroelectric
materials in their ferroelectric phase are pyroelectrics and piezoelectrics. Table 1 lists based
properties of some of the more commonly used ferroelectric materials (Settera, 2006).

6
3. Physical principle AFeRAM device operation
Ferroelectric crystals are a subgroup of piezoelectric materials. It means that all ferroelectric
materials are piezoelectric. Some ferroelectrics are excellent piezoelectrics (see Table 1). It is
known that piezoelectric materials can generate useful output under simple input signal.
For example, piezoelectric material will generate an electric field with the input of stress or
vice versa.
The piezoelectric effect is a natural ability of piezoelectric materials to produce an electric
charge, which is proportional to an applied mechanical stress. This is termed the direct
piezoelectric effect. By reversing the direction (from tension to compression) of the stress
applied to piezoelectric material, a sign of the created electric charge is reversed as well. The
piezoelectric effect is also reversible. When an electric charge or voltage is applied, a
mechanical strain is created. This property is called the inverse piezoelectric effect. In other
words, when piezoelectric film is stressed electrically by voltage, its dimensions change and
generate acoustic wave. When it is stressed mechanically by force or acoustic wave, it
generates an electric charge. If electrodes are not short-circuited, voltage associated with the
charge appears. Both piezoelectric effects are used in AFeRAM devices.
A basic characteristic of piezoelectric materials is the piezoelectric charge constant (d). The
piezoelectric charge constant, d (C/N), is the polarization generated per unit of mechanical
stress applied to a piezoelectric material or, alternatively, the piezoelectric charge constant,
d (m/V), is the mechanical strain experienced by a piezoelectric material per unit of applied
electric field (1).
( ) ( )
Charge density Strain developed
C/N m/V
Applied mechanical stress Applied electric field
= = d (1)
In general, since piezoelectric charge constant is a second-rank tensor value, it is correct to
write d in the equations as the tensor components; in the case of polycrystalline thin films
we deal with the effective value of piezoelectric charge constant, d
eff
. Sometimes notation d
33

is also used to represent piezoelectric charge constant measured in the direction
perpendicular to film surface.
Piezoelectric charge constant (d
33
) is an important characteristic of the material’s suitability
for AFeRAM device. Others are Young’s (or elastic) modulus (Y), electromechanical
coupling factor (K), and dielectric constant (ε). Y is an indicator of the stiffness (elasticity) of
a material. Typical value of the bulk piezoelectric charge constant, d
33
(C/N) for several
fully poled conventional ferroelectric materials are tabulated in Table 1. At the same time, it
is known that piezoelectric charge constants of ferroelectric thin films (100 nm or less)
increase in several times for feature sizes of cells with lateral dimensions below 300 nm
(Buhlmann, & et al, 2002).
There are two methods for determining a value and polarity of the intrinsic remanent
polarization of memory cells by piezoacousto approach. The first one, the ferroelectric
memory cell is stressed mechanically by pulse force or acoustic solitary wave and then the
momentarily generated electric charge in the ferroelectric memory cell is measured by
conventional methods or with the use of FeFET as memory element.
The second method is to measure the generated acoustic elastic solitary wave, when the
ferroelectric memory cell is stressed electrically by the reading voltage pulse with special
waveform. As it was mentioned before, the field effect transistor with piezoelectric gate can
Principle Operation of 3–D Memory Device
based on Piezoacousto Properties of Ferroelectric Films

7
be used for detecting the acoustic solitary wave, which is generated by the ferroelectric
memory cell under the action of the reading voltage pulse.
The most obvious advantage of the second method is that the memory cells are not directly
connected to the access and sensitive and measuring transistor by conductor wires, but
exchange data with the access transistor by acoustic solitary waves. It means that there is an
acoustic interconnection between the ferroelectric memory cells and the access transistor,
which allows creating 3–D structure of memory device without using additional metal
interconnections.

Fig. 1. Simplified structure and principle operation of AFeRAM element
In simple case, the AFeRAM element has a columnar structure (Fig. 1). The structure of the
AFeRAM element can be implemented using two well know devices: a) ferroelectric
capacitor or capacitors which acts as ferroelectric memory cell where two binary logic states
“0” and “1” are represented by the direction of the spontaneous polarization as well as
piezoacoustic transmitter; b) field effect transistor with piezoelectric or polarized
ferroelectric gate which acts as acoustic sensor and access transistor. The memory cell or
cells are stacked above the transistor with the piezoelectric-ferroelectric gate. The memory
cells are merged with the access transistor with ferroelectric/ piezoelectric gate to form
AFeRAM element. At the same time, memory cells have no electrical link to the access
transistor. Ferroelectric memory cell and the access transistor exchange the information by
an acoustic elastic solitary deformation wave (Fig. 1).
There is vague similarity between the AFeRAM element and piezoelectric transformer. The
direct and converse piezoelectric effects are used in AFeRAM memory element as well as in
the piezoelectric transformer, where voltage from one unit (in our case, from memory cell)
to another (in our case, to transistor gate) is transformed acoustically.
The memory cell can be programmed in accordance with the conventional method by
applying high negative electrical field (state of “0”) or positive electrical field (state of “1”) to
the memory cell (Fig. 1).
In order to read the stored information, reading pulse voltage (V
R
MC
) weaker than the
coercive voltage is applied to the memory cell, and two types of acoustic elastic solitary
deformation waves can be generated. For example, the reading electrical field, additive to
the ferroelectric memory cell polarization (state “1”), will produce a tensile stress. The
Ferroelectrics

8
reading electrical field, opposite to the ferroelectric memory cell polarization (state “0”), will
produce a compressive stress. In turn, these stresses produce the acoustic solitary wave,
which produces stress on the piezoelectric-ferroelectric gate of the access transistor. This
stress produces a momentary “polarization” (ΔP) of the transistor piezoelectric-ferroelectric
gate and controls channel conductivity of the transistor. Positive piezoelectric charges
increase the effective donor concentration, reducing thickness of the surface depletion layer.
Therefore, the conductivity of the semiconductor channel can be altered by the momentary
piezoelectric charge due to acoustic solitary wave when it goes through the ferroelectric
gate. The reading operation is thus carried out by identifying whether the current flows
from the source to the drain of the transistor (state “1”) or not (state “0”) or vice versa. The
memory cells exchange data with the access transistor by means of acoustic solitary waves.
The momentary generated charges or polarization can be relatively easily calculated in
terms of piezoelectric and elastic constants. Equation for the value of the momentary
generated charges or polarization is as follows:
ΔP = d
33
TG
· d
33
MC
· Y
MC
· V
R
MC
; (2)
Here ΔP (μC/cm
2
) is the momentarily generated charge or polarization within the transistor
gate; d
33
TG
and d
33
MC
are the piezoelectric charge constants for the transistor gate (TG) and
memory cell materials (MC), respectively; Y
MC
is the Young modulus for the memory cell
materials and V
R
MC
is the reading voltage applied to the memory cell. The momentary
polarization calculated within the transistor gate for different materials of the fixed memory
cell and the transistor gate are presented in Table 2.
Typical thicknesses of the memory cell and the transistor gate film are 100 nm, and the
reading voltage (V
R
MC
) is about 0.5 V. As shown in Table 2, the momentary polarization of
the piezoelectric gate can exceed several times the critical value of polarization (0.1–0.2
μC/cm
2
) required for the transistor functioning (Miller, 1992; Dawber, 2005).

Materials for ferroelectric memory cells
Materials
for ferroelectric
transistor gates
LiNbO
3
SBT BiFeO
3
PZT
PZT 0.25–1.72 0.47–1.0 1.22–2.25 2.25–9.0
PMN-PT 1.50–2.25 2.80–4.30 7.50–11.25 15.0–45.0
Table 2. Momentary polarization ΔP(μC/cm
2
) generated within the ferroelectric-
piezoelectric transistor gate by solitary acoustic wave
It shows a very high acoustic wave sensitivity of FeFET with ferroelectric/piezoelectric gate
which allows using a broad assortment of the ferroelectric materials with low value of an
intrinsic remanent polarization of ferroelectric memory cells and low temperature
deposition for memory cells as well as for ferroelectric/piezoelectric gate; to create 3–D
structure of memory device with many memory cell layers stacked above the access
transistor and to operate on a multi-bit mode to store more than one bit per memory cell
(Kimura H., Hanyu T. & Kameyama M. 2003).
Another advantageous way to detect the acoustic solitary wave is to use an access and
acoustic sensing transistor based on ferroelectric or piezoelectric semiconductors (e.g. GaAs,
Principle Operation of 3–D Memory Device
based on Piezoacousto Properties of Ferroelectric Films

9
GaN, AlN) or their heterostructure (e.g. GaAs/AlGaAs, GaN/AlN) which characterised fast
the channel transit time (Kang Y., Fan Q., Xiao B. & et al., 2006; Lu S. S. & Huang C.L., 1994;
Wu & Singh, 2004). In both cases the transistor channel charge and current are controlled by
the gate voltage and/or by acoustic solitary wave.
Ferroelectric materials with high piezoelectric charge constants for transistor gate, like PZT
or PMN-PT; and “fatigue-free” ferroelectric materials with relatively small piezoelectric
charge and dielectric constant for memory cell, like LiNbO
3
or SBT, can be recommended.
The most obvious advantage of detecting direction and value of the polarization of
ferroelectric memory cells by acoustic solitary wave is that the memory cells are not directly
connected to access and acoustic sensing transistor by conductor wires. It allows easy
creating 3–D structure of memory device by stacking the several layers of memory cells
above array of the access transistors without using additional metal interconnections.
One of the main issues of AFeRAM devices is the echo phenomena. This problem can be
eliminated and neglected by using composite packed materials with high acoustic
absorption factor and acoustical impedance value equal to the silicon acoustical
impedance.
4. 3-D architectures of Acousto-Ferroelectric RAM
There are several types of the AFeRAM memory storage element structures and operation
modes. Basically, the AFeRAM element consists of two parts: saving (memory) area
(ferroelectric memory cell or cells) and reading area (a ferroelectric field transistor) (Fig. 2,
3). There is perfect analogy between reading area of AFeRAM element and FeFET memory
devices. It means that FeFET can be used as a parent element of AFeRAM memory devices.
Moreover design problems for AFeRAM are already known very well and have been solved
by FeFET and other FeRAM device solutions (Wang S. & et al. 2009). Furthermore, the new
principle for ferroelectric memory operation does not have great demands to the remanent
polarization and conductivity of the submicron ferroelectric film. It allows easy finding of
new candidate ferroelectric materials for AFeRAM devices (Settera, 2006).
One of promising structures of memory elements (resembling the NAND Flash
configuration) are shown in Fig. 2. In these structures, the memory area consists of cross
point memory ferroelectric cells and the memory cell size is determined by crossing array
between the top and bottom electrodes (Fig. 2). This memory area is relatively simple to
manufacture, as one involve only three layers of metal and two ferroelectric layers
sandwiched between metal strips. In this case, patterning of a submicron ferroelectric film is
not needed for the memory cells. It is easy to create two levels and inexpensive memory
device. Fig. 2a shows an equivalent electrical circuit of the two-layer memory area. The
reading area of this type of AFeRAM element consists of FeFET with an elongated
conductance channel and multi metal gate.
Another promising structure of a three-layer memory element is shown in Fig. 3. Fig. 3a
shows an equivalent electrical circuit of the three-layer memory area. In these structures, the
memory area also consists of cross point ferroelectric memory cells which are separated by
dielectrics with different values of acoustical impedance and dielectric constant. It allows
creating acoustic channels, improving anisotropy of solitary acoustic wave propagation in
the stratified structure and eliminates acoustic cross talk. In these cases the reading area of
AFeRAM element also consists of the piezoelectric/ferroelectric field transistor with the
elongated conductance channel and the multi-metal gate.
Ferroelectrics

Fig. 3. Three-layer AFeRAM structure with elongated a conductance channel of access
transistors. The memory cells are separated by different type of dielectrics and form acoustic
channels
This type of memory element allows creating practically unlimited number of memory cell
layers and can be easily scaled down to tens of nanometers electrode stripe width and use
nano-ferroelectric materials (Scott , 2006).

First memory layer Third memory layer Second memory layer

Fig. 3a. Equivalent electrical circuit for the three-layer memory area
Principle Operation of 3–D Memory Device
based on Piezoacousto Properties of Ferroelectric Films

11
The AFeRAM element architecture allows stacking more than one layer (four or six layers)
of memory arrays (3–dimensional stacking), offers scalability, the simplest and lowest cost
technology and the highest integration density (∼10 Gbit/cm
2
for F=90 nm or ∼100 Gbit/cm
2

for F=32 nm and four layers of memory arrays, where F denotes the smallest feature size
limited by lithography resolution). The additional increase in info density can be reached by
means of a multi-bit mode to store more than one bit per memory cell (Kimura, Hanyu &
Kameyama, 2003).
5. Operation modes of Acousto-Ferroelectric RAM
A memory area of all type of AFeRAM elements consist of cross point ferroelectric memory
arrays. The cross point memory arrays are relatively simple to manufacture, as they only
involve two layers of metal and some ferroelectric layer sandwiched between. They
typically have high density. The electrodes are typically arranged in an X and Y conductive
strips, with each cell of the cross point array being located at the points in the ferroelectric
materials where the X and Y strips cross over each other. The data bit stored in each cell has
a value determined by the polarity of the ferroelectric material at that point. The polarity is
controlled by application of voltages on the X and Y strips. Typically, the X strips are
referred to as word lines and the Y strips are referred to as bit lines. Write operations and
read operations are normally accomplished by applying voltages to the word line and bit
line of the cell. In this case, ferroelectric capacitors can form a ferroelectric memory array in
the same way as magnetic cores form a core memory.
5.1 Writing operation modes
Writing operation modes will be illustrated by the example of the two-layer AFeRAM
structure with elongated conductance channel (Fig. 2). As it was mentioned above, the
ferroelectric memory cells of AFeRAM element can be programmed with conventional
method (Fig. 2a) by applying a high negative electrical field (state of “0”) or positive
electrical field (state of “1”) to the memory cell. In order to program the ferroelectric
memory cell, the program voltage (V
Pr
) across the ferroelectric capacitor must exceed the
coercive voltage (V
C
), hence, V
Pr
>= V
C
.

12
There are two voltage pulse protocols to write information into the ferroelectric memory
cells which are the 1/2V protocol and the 1/3V protocol. Despite the fact that passive
memory array is relatively small, a voltage pulse protocol based on the 1/3 voltage selection
rule (1/3V protocol) should be used in order to keep disturb voltages at minimum (Fig. 2a).
It is possible to write data to multiple cells in both schemes; word line by word line (Fig. 2a)
or bit line by bit line, but this cannot be performed simultaneously for the “l“ state and
“0”states.
To write a “0” state by using the 1/3V protocol, the corresponding bit line of the cells to be
written is connected to V
Pr
and the corresponding word line to V=0. All other bit lines are
connected to 1/3V
Pr
and all other word lines to 2/3V
Pr
as can be seen in Fig. 2a. The voltage
drop on all non accessed cells is 1/3V
Pr
or -1/3V
Pr
, which means, that the distortion voltage
is reduced in comparison to the 1/2V protocol. Writing a "1" is similar but this time the
voltages of the word lines and bit lines are exchanged (Fig. 2b). The three-layer as well as
multi-layers AFeRAM devices would operate in much the same manner as analogously to
the two-layer AFeRAM elements.

Fig. 2b. Equivalent electrical circuit for the two-layer memory area and writing mode
(program “1” state)
As it was mentioned before, the one of important features of FeFET which uses as reader of
the polarization memory cell is its high sensitivity to a mechanical stress or acoustic waves
(Greeneich & Muller, 1975). It allows using a low voltage to program memory cell.
Therefore, it should be possible to use value of the program voltage very closely to the
coercive voltage V
C
as soon as possible. As result endurance can be increase to up 10
15-17

(Joshi, 2000). It allows using AFeRAM element as DRAM device. Moreover, the low
switching voltages for programming is a definitive advantage for low-power applications,
system management issues, and scalability.
5.2 Reading operation modes
Reading operation modes will be illustrated by the example of the three-layer AFeRAM
structure with elongated conductance channel and multi-gate field effect transistor (Fig. 3).
The reading operation mode of for the three-layer memory area of AFeRAM memory
element is shown in Fig. 3b, 3c. In order to information read-out from AFeRAM element; the
reading pulse voltage (V
R
) weaker than the coercive voltage is applied sequentially to the
memory cells (a, b, c, and d) (Fig. 3b, 3c).
Principle Operation of 3–D Memory Device
based on Piezoacousto Properties of Ferroelectric Films

Fig. 3c. Timing diagram of the reading pulse voltages for each of the memory cells (a, d, c
and d on Fig. 3b), amplitude of solitary acoustic wave generated by memory cells and the
corresponding source-drain current through the semiconductor channel of the access
transistor
Fig. 3c shows a timing diagram of the reading pulse voltages with special waveform for
each of the memory cells, its acoustic response under the action of the reading pulse
voltages and the corresponding current through the semiconductor channel of the access
transistor. Initially, the access transistor is opened by metal gates and the maximum current
flows easy from the source to the drain of the access transistor (Fig. 3c). Two types of
acoustic elastic solitary deformation waves (or shock waves) can be generated (Fig. 3c) by
Ferroelectrics

14
memory cells. Memory cell (state “1”) will produce a tensile acoustic solitary wave and
memory cell (state “0”) will produce a compressive acoustic solitary wave under the action
of the positive reading pulse (Fig. 3c). In turn, only compressive acoustic solitary wave
which are generated (Fig. 3c) by memory cells (b and d) (state “0”) produce the positive
momentary “polarization” (ΔP) of the transistor ferroelectric gate and interrupts current
through the semiconductor channel of the access transistor. The reading operation is thus
carried out by identifying interrupt of current through the semiconductor channel of the
access transistor by check out state “0” of memory cells (Fig. 3c).
The memory cells exchange data with the access transistor by means of acoustic solitary
waves. The highest frequency exchange data between the memory cell and the sensitive
transistor can extend to the GHz range (Greeneich & Muller, 1975) and is determined by the
transistor frequency response and ultimately by the channel transit time.
The piezoacousto approach also allows us to use a parallel reading without distortion of
nonselected cells, bit line by bit line (Fig. 2c, 3c). These modes effectively reduce the
programming and reading time per byte by factor of 16 or 64 or more. This factor is
determined by size of the memory array. It is also important to notice that the reading and
programming periphery circuits of the passive memory array are the same.
6. Conclusion
In order to improve the performance and scalability of today’s memory devices, a lot of new
memory technologies are under investigation now. The goal these investigations to find the
ultimate universal memory that combines fast read, fast write, non-volatility, low-power,
unlimited endurance and high info density.
Forecasting the future of solid state memory leads us to the inescapable conclusion that
lithographic scaling becomes more challenging and memory companies should be turning
their sights to investigation of 3-D memory technology based on stackable cross-point
memory arrays. At the same time, in 3-D memory architecture, current-driven memory
devices with high power dissipation which is developing now can not be used.
Today it is known only one physical principle operation of a voltage-controlled memory
device with low power consumption and dissipation; it is ferroelectric memory with
intrinsic memory phenomenon. Unfortunately, reading operation mode of conventional
FeRAM devices which are developed and manufactured now do not use all good
performances of the ferroelectric memory phenomenon and its lithographic scaling becomes
more challenging beyond the 90 nm node.
The AFeRAM concept uses the two physical properties of a ferroelectric film (two-in-one),
the intrinsic memory phenomenon for information storage and piezoacousto property for
effective read-out info. It allows the design and implementation of 3-D memory devices
with universal characteristics of the inherent ferroelectric memory. Furthermore, there is no
limitation in future AFeRAM miniaturization in the sense of the operational principle and
can be shrunk down into the nanometer range that is a great advantage compared to
current-controlled memory devices. Acoustic principle of ferroelectric memory operation
does not require high remanent polarization value and value of conductivity of a submicron
ferroelectric film. It allows us to easily find a new candidate among ferroelectric materials.
Very high acoustic wave sensitivity of the FeFET with ferroelectric gate allows us to use a
wide range of ferroelectric materials or use an access and acoustic sensing transistor based
on ferroelectric or piezoelectric semiconductors, which characterised fast the channel transit
Principle Operation of 3–D Memory Device
based on Piezoacousto Properties of Ferroelectric Films

16
Kimura H., Hanyu T. & Kameyama M. (2003). Multiple-Valued Logic-in-Memory VLSI
Using MFSFETs and its Applications. Journal of Multiple-Valued Logic and Soft
Computing Vol. 9, pp. 23-42.
Krieger Ju. H. (2008). Acousto-ferroelectric nonvolatile RAM, Integrated Ferroelectrics, Vol. 96,
No. 1, pp. 120–128.
Krieger Ju. H. (2009). Physical concepts of FeRAM device operation based on piezoacousto
and pyroelectric properties of ferroelectric films. Journal Applied Physics, Vol. 106,
No. 6, pp. 0616291–0616296.
Lu S. S. & Huang C.L. (1994). Piezoelectric field effect transistor (PEFET) using
In0.2Ga0.8As/Al0.35Ga0.65As/In0.2Ga0.8As/GaAs strained layer structure on
(111)B GaAs substrate. Electronics Letters, Vol. 30, No. 10, p. 823-825.
Miller S. L. & McWhorter P. J. (1992). Physics of the ferroelectric nonvolatile memory field
effect transistor, Journal Applied Physics, Vol. 72, No. 12, pp. 5999–6010.
Park K-T., Kang M., Hwang S. & et al. (2009). A fully performance compatible 45 nm 4-
gigabit 3–D double-stacked multi-level NAND flash memory with shared bit-line
structure. IEEE Journal of Solid-State Circuits, Vol. 44, No. 1, pp. 208–216.
Park S. O., Bae B. J., Yoo D. C. & Chung U. I. (2010). Ferroelectric random access memory.
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Journal Electrochemical Society, Vol. 151, No. 6, pp. K13-K19.
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Matter, Vol.18, pp. R361–R386.
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51606–51646.
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ferroelectric (Fe)-NAND flash memory array. Semiconductor Science and Technology,
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0
Ferroelectric and Multiferroic Tunnel Junctions
Tianyi Cai
1
, Sheng Ju
1
, Jian Wang
2
and Zhen-Ya Li
1
1
Department of Physics and Jiangsu Key Laboratory of Thin Films
Soochow University, Suzhou, 215006
2
Department of Teaching Affairs,
Wuxi City College of Vocational Technology, Wuxi, 214153
China
1. Introduction
The phenomenon of electron tunneling has been known since the advent of quantum
mechanics, but it continues to enrich our understanding of many ﬁelds of physics, as well
as offering a route toward useful devices. A tunnel junction consists of two metal electrodes
separated by a nanometer-thick insulating barrier layer, in which an electron is allowed
to transverse a potential barrier exceeding the electron’s energy. The electron therefore
has a ﬁnite probability of being found on the opposite side of the barrier. In the 1970’s,
spin-dependent electron tunneling from ferromagnetic metal electrodes across an amorphous
Al
2
O
3
ﬁlm was observed by Tedrow and Meservey(1)(2). Based on this discovery, Julli` ere
proposed and demonstrated that in a magnetic tunnel junction tunnel current depends on the
relative magnetization orientation of the two ferromagnetic electrodes(3). Such a phenomenon
nowadays is known as tunneling magnetoresistance(TMR)(4). Magnetic tunnel junctions may
be very useful for various technological applications in spintronics devices such as magnetic
ﬁeld sensors and magnetic randomaccess memories. Other insulators are also used for tunnel
barriers. For example, epitaxial perovskite SrTiO
3
barriers were studied by De Teresa et
al. to demonstrate the importance of interfaces in spin-dependent tunneling(5). In tunnel
junctions with MgO barriers, Ikeda et al. found large magnetoresitance as high as 604% at
roomtemperature and 1144% at 5 K(6), which approaches the theoretical predictions of Butler
et al.(7) and Mathon et al.(8). Despite the diversity of materials used as the barrier of the tunnel
junctions, the common feature is that almost all the barriers are nonpolar dielectrics.
On the other hand, magnetic insulators, i.e, EuO, EuS and EuSe, are used for tunnel barriers.
Spin ﬁltering has been observed in these junctions as were ﬁrst discussed by Moodera et
al.(9). in 1988. They observed that the tunneling current in Au/EuS/Al junction has a spin
polarization with the magnitude as high as 80%. and attributed it to the electron tunneling
across the spin-dependent barriers (Fig.1). Later, they reported that the tunneling current
across Ag/EuSe/Al junctions has an enhanced spin-polarization reaching 97%(10). Recently,
using EuO with a higher Curier temperature (69 K) than EuS (16.7 K) and EuSe (4.6 K),
Santos et al. obtained 29% spin-polarized tunneling current(11). Naturally, if electrodes
are not normal metals, but ferromagnetic materials, both TMR and spin ﬁlter effects can be
observed(Fig.2)(12).
Another important concept is the ferroelectric tunnel junction (FTJ)(13)(14)(15), which take
advantage of a ferroelectric as the barrier material. Ferroelectrics possess a spontaneous
2
2 Ferroelectrics
Fig. 1. Schematic illustration of tunnel barrier of a Au/EuS/Al junction. W
1
and W
2
are the
work functions of Au and Al, respectively. χ is the electron afﬁnity of EuS. The barrier
heights at the Au and Al interfaces are shown as Φ
1
and Φ
2
at the bottom of the EuS
conduction band (dashed line) at T>16.7 K. The bottom of the two bands shown at T ≤ T
C
by
the solid lines separated by ΔE
ex
are the barriers seen by the two spin directions.(9)
electric polarization that can be switched by an applied electric ﬁeld. This adds a new
functional property to a tunnel junction. Nowadays, there are worldwide efforts to include
FTJs into various nanoscale devices such as Gbit nonvolatile semiconductor memories. This
Fig. 2. Schematic illustration of spin ﬁltering and the MR effect. (a) above T
C
of the EuS ﬁlter
the two spin currents are equal. (b) below the T
C
of EuS, the tunnel barrier is spin split,
resulting in a highly spin polarized tunnel current. With a ferromagnetic (FM) electrode, the
tunnel current depends on the relative magnetization orientation. For parallel alignment (P),
(c) a large current results, while for antiparallel alignment (AP), (d) a small current
results.(12)
18 Ferroelectrics
Ferroelectric and Multiferroic Tunnel Junctions 3
may open new exciting perspectives but also give rise to important fundamental questions.
For example, can ferroelectricity exist in a nanometer-thick barrier ﬁlm? As is well-known,
ferroelectricity is a collective phenomenon (as magnetism or superconductivity) and it results
from a delicate balance between long-range Coulomb forces (dipole-dipole interaction)
which are responsible for the ferroelectric state and short-range repulsion which favor the
paraelectric cubic state. When the size of a ferroelectric sample is reduced, both Coulomb
and short-range forces are modiﬁed. This leads to a behavior at very small size that cannot be
trivially predicted and causes eventually a suppressionof the interesting functional properties
below what is referred to the correlation volume. The ferroelectric instability of ultra-thin
ﬁlms and ultra-small particles has been an open question for several decades. Recently,
experimental and theoretical investigations showed that ferroelectricity may persist even at
a ﬁlm thickness of a few unit cells under appropriate mechanical (lattice strain) and electric
boundary (screening) conditions. In particular, it was discoveredthat, in organic ferroelectrics,
ferroelectricity can be sustained in thin ﬁlms of a few monolayer thickness (16). In perovskite
ferroelectric oxides, ferroelectricity was observed down to a nanometer scale (17). This fact
is consistent with ﬁrst-principle calculations that predict a nanometer critical thickness for a
FTJ (18). As a result, the existence of ferroelectricity at such a small ﬁlm thickness makes it
possible to use ferroelectrics as tunnel barriers.
Let us now turn to a general outline of this chapter. We will begin with a discussion of
the concept of a ferroelectric tunnel junction, then show that the reversal of the electric
polarization in the ferroelectric produces a change in the electrostatic potential proﬁle across
the junction. This leads to the resistance change which can reach a few orders of magnitude,
namely, the giant tunneling electroresistance (TER) effect. Interface effect, strain effect and
composite barrier are also discussed. Next, we will show that functional properties of FTJs
can be extended by adding the spin degree of freedom to FTJs. This makes the junctions
multiferroic (that is, simultaneously ferromagnetic and ferroelectric). The interplay between
ferroelectric and magnetic properties in a multiferroic tunnel junction (MFTJ) may affect
the electric polarization of the ferroelectric barrier, the electronic and magnetic properties
of the interface, and the spin polarization of the tunneling current. Therefore, TMR and
spin ﬁltering effect observed in MTJs can also be observed in MFTJs. Such a new kind
of tunnel junction may be very useful for future technological applications. Several ways
to obtain MFTJs are introduced, such as (1) replacing one normal metal electrode with
ferromagnetic one, (2) replacing ferromagnetic barriers with multiferroic materials, and (3)
using a composite of ferromagnets and ferroelectrics as the barrier. These studies open an
avenue for the development of novel electronic devices in which the control of magnetization
can be achieved by the electric ﬁeld via magnetoelectric coupling. Finally, we look at the
magnetoelectric coupling effect in the ferroelectric-based junctions, which is independent of
particular chemical or physical bonding.
2. Ferroelectric tunnel junction
The concept of a FTJ is illustrated in Fig.3(15), which shows the simpliﬁed band structure of a
tunnel junction with a ferroelectric barrier. If the ferroelectric ﬁlm is sufﬁciently thin but still
maintains its ferroelectric properties, the surface charges in the ferroelectric are not completely
screened by the adjacent metals [Fig.4(a)] and therefore the depolarizing electric ﬁeld E in the
ferroelectric is not zero. The electrostatic potential associated with this ﬁeld depends on the
direction of the electric polarization [Fig.4(b)]. If a FTJ is made of metal electrodes which
have different screening lengths, this leads to the asymmetry in the potential proﬁle for the
19 Ferroelectric and Multiferroic Tunnel Junctions
4 Ferroelectrics
Fig. 3. (Color online). Schematic diagram of a tunnel junction, which consists of two
electrodes separated by a nanometer-thick ferroelectric barrier layer(15). (E
gap
is the energy
gap. E
F
is the Fermi energy, V is the applying voltage, t is the barrier thickness.)
opposite polarization directions. Thus, the potential seen by transport electrons changes with
the polarization reversal which leads to the TER effect.
Electrostatic effect. The above arguments can be made quantitative by applying a
Thomas-Fermi model. The screening potential within metal 1 and metal 2 electrode is given
by(19)
ϕ(z) =

σ
S
δ
L
e
−|z|/δ
L
ε
0
, z ≤0
−
σ
S
δ
R
e
−|z−d|/δ
R
ε
0
, z ≥ d
(1)
Here δ
L
and δ
R
are the Thomas-Fermi screening lengths in the M
1
and M
2
electrodes. σ
S
is the
magnitude of the screening charges and can be found from the continuity of the electrostatic
potential:
ϕ(0) − ϕ(d) =
d(P −σ
S
)
ε
F
(2)
Here P is considered to be the absolute value of the spontaneous polarization, and the
introduction of the dielectric permittivity ε
F
is requiredto account for the induced component
of polarization resulting from the presence of an electric ﬁeld in the ferroelectric. Using
Eqs.(1)-(2) and introducing the dielectric constant ε = ε
F
/ε
0
, σ
S
can be expressed as σ
S
=
dP/[ε (δ
L
+ δ
R
) + d].
Figure 4(b) shows the electrostatic potential in a M
1
-FE-M
2
junction assuming that metals
M
1
and M
2
have different screening lengths, such that δ
L
> δ
R
. It follows from Eq.(1) that
different screening lengths result in different absolute values of the electrostatic potential at
the interfaces, so that ϕ
1
≡ |ϕ(0)| = ϕ
2
≡ |ϕ(d)|, which makes the potential proﬁle highly
asymmetric. The switching of the polarization in the ferroelectric layer leads to the change in
the potential which transforms to the one shown in Fig.4(b) by the dashed line, thus, inevitably
leading to the change in the resistance of the junction.
20 Ferroelectrics
Ferroelectric and Multiferroic Tunnel Junctions 5
Tunneling electroresistance effect. If the thickness of the ferroelectric barrier is so small that
the dominant transport mechanism across the FTJ is the direct quantum-mechanical electron
tunneling. The conductance of FTJ can be calculated, for example, at a small applied bias
voltage the conductance of a tunnel junction per area A is(20)
G
A
=
2e
2
h

d
2
k

(2π)
2
T

E
F
, k

(3)
Here, T is the transmission coefﬁcient evaluated at the Fermi energy E
F
for a given value of
the transverse wave vector k

, which can be obtained from the Schr¨ odinger equation for an
electron moving in the potential.
The overall potential proﬁle seen by the transport electrons is a superposition of the
electrostatic potential shown in Fig.4(b), the electronic potential which determines the bottom
of the bands in the two electrodes with respect to the Fermi energy E
F
, and the potential
barrier created by the ferroelectric insulator. The resulting potential for the two opposite
orientations of polarization in the ferroelectric barrier is shown schematically in Fig.5 for
Fig. 4. Electrostatics of a M
1
-FE-M
2
junction: (a) charge distribution and (b) the respective
electrostatic potential proﬁle (solid line)(14). The polarization P creates surface charge
densities, ±σ
P
= ±|P|, on the two surfaces of the ferroelectric ﬁlm. These polarization
charges ±σ
P
, are screened by the screening charge per unit area, ∓σ
S
, which is induced in the
two metal electrodes. It is assumed that metal 1 (M
1
) and metal 2 (M
2
) electrodes have
different screening lengths (δ
L
> δ
R
) which lead to the asymmetry in the potential proﬁle.
The dashed line in (b) shows the potential when the polarization P in the ferroelectric is
switched, resulting in the reversal of the depolarizing ﬁeld E. The following assumptions are
made: (1) The ferroelectric is assumed to be uniformly polarized in the direction
perpendicular to the plane. (2) The ferroelectric is assumed perfectly insulating so that all the
compensating charges resides in the electrodes. (3) The short-circuited FTJs are discussed.
21 Ferroelectric and Multiferroic Tunnel Junctions
6 Ferroelectrics
Fig. 5. Schematic representation of the potential proﬁle V(z) in a M
1
-FE-M
2
junction for
polarization pointing to the left (a) and for polarization pointing to the right (b), assuming
that δ
1
> δ
2
. The dashed lines show the average potential seen by transport electrons
tunneling across the ferroelectric barrier(14). The horizontal solid line denotes the Fermi
energy, E
F
.
δ
L
>δ
R
. Indeed, the average potential barrier height seen by the transport electrons travelling
across the ferroelectric layer for polarization pointing to the left, U
L
= U + (ϕ
1
− ϕ
2
)/2,
is not equal to the average potential barrier height for polarization pointing to the right,
U
R
= U + (ϕ
1
− ϕ
2
)/2, as is seen from Figs. 5(a) and 5(b). This make the conductance G
L
for polarization pointing to the left much smaller than the conductance G
R
for polarization
pointing to the right (Fig.6(a)), thereby resulting in the TER effect(Fig. 6(b))(14).
Experimentally, ferroelectric tunnel junctions with different ferroelectric barriers have been
fabricated successfully and giant tunneling electroresistance effects have been observed.
Garcia et al.(21) and Gruverman et al.(22) reported that giant TER effects reached 75000%
through 3 nm-thick BaTiO
3
barrier at room temperature. Crassous et al. observed that the
TER reached values of 50000% through a 3.6 nm PbTiO
3
(23). Maksymovych et al. found
Fig. 6. (a) conductance per unit area for polarization oriented to the right, G
R
/A (solid line)
and for polarization oriented to the left, G
L
/A (dashed line); (b) conductance change,
G
R
= G
L
, associated with the polarization switching in the ferroelectric barrier (14). The
vertical dotted line indicates the value of δ
1
= δ
2
at which no asymmetry in the potential
proﬁle and, hence, no conductance difference is predicted.
22 Ferroelectrics
Ferroelectric and Multiferroic Tunnel Junctions 7
Fig. 7. Interface effect of a FTJ (15).
that the large spontaneous polarization of the Pb(Zr
0.2
Ti
0.8
)O
3
ﬁlm resulted in up to 500-fold
ampliﬁcation of the tunneling current upon ferroelectric switching(24).
Interface and strain effect. Interestingly, recent experimental(25) and theoretical(26) studies
indicate that ionic displacements within the electrodes, in a few atomic monolayers adjacent
to the ferroelectric, may affect the electron screening. The polarization switching alters
positions of ions at the interfaces that inﬂuences the atomic orbital hybridizations at the
interface and hence the transmission probability (see Fig.7). On the other hand, the
piezoelectricity of a ferroelectric barrier under an applied voltage produces a strain (see
Fig.8) that changes transport characteristic of the barrier such as the barrier width and the
attenuation constant(27).
FTJs with ferroelectric/dielectric composite barriers. It is an efﬁcient way to enhance the TER by
using a layered composite barrier combing a functional ferroelectric ﬁlm (FE) and a thin ﬁlm
of a nonpolar dielectric material (DI)(28). Due to the change in the electrostatic potential
Fig. 8. Strain effect of a FTJ (15).
23 Ferroelectric and Multiferroic Tunnel Junctions
8 Ferroelectrics
Fig. 9. (Color online) Geometry (a) and the electrostatic potential proﬁle for the two opposite
polarization orientations (b) of a FTJ: a=25
˚
A, b=5
˚
A, ε
d
=300, ε
f
=90, δ =1
˚
A, and P=20
μC/cm
2
(28).
induced by polarization reversal, the nonpolar dielectric ﬁlm adjacent to one of the interfaces
acts as a switching changing its barrier height from a low to high value (Fig.9), resulting in
a dramatic change in the transmission across the FTJ. The predicted values of TER are giant,
indicating that the resistance ratio between the two polarization-orientation states in such FTJs
may reach hundred thousands and even higher as shown in Fig.10. Furthermore, Wu et al.
proposed that if the interface between the FE and the dielectric layer is very sharp and space
charges exist at this interface, the TER will be enhanced strongly(29).
Fig. 10. (Color online) (a) Conductance of a FTJ for two opposite polarization orientations:
Left (solid line) and right (dashed line), as a function of dielectric layer thickness. The insets
show the corresponding tunneling barrier proﬁles. (b) TER as the function of dielectric layer
thickness for two polarizations P=20 μC/cm
2
(solid line) and P=40 μC/cm
2
(dashed line).
The inset shows TER as the function of the ferroelectric ﬁlm thickness. U
d
=0.6 eV, ε
d
=300(28).
24 Ferroelectrics
Ferroelectric and Multiferroic Tunnel Junctions 9
It should be noted that FTJs with composite barriers (M/FE/DI/M) does not require different
electrodes. This may be more practical for device application than the conventional FTJs
(M
1
/FE/M
2
). For FTJs as M
1
/FE/M
2
, asymmetry is necessary for the TER effect, which may
be intrinsic (e.g., due to nonequivalent interfaces) or intentionally introduced in the system
(e.g., by using different electrodes).
3. Multiferroic tunnel junctions (MFTJ)
A MFTJ is simultaneously ferromagnetic and ferroelectric. The transport behaviors of
MFTJs can be controlled by the magnetic and electric ﬁeld. Furthermore, the interplay
between ferromagnetic and ferroelectric properties may affect the electric polarization of the
ferroelectric barrier, the electronic and magnetic properties of the interface, and the spin
polarization of the tunneling current. This indicates that not only TER effect, TMR and spin
ﬁltering effects may also be observed in MFTJs.
3.1 Ferromagnet/ferroelectric/normal metal junctions
By replacing normal metal electrode with a highly spin-polarized (ferromagnetic) material,
such as diluted magnetic semiconductor(30), doped manganite(31), double perovskite
manganites, CrO
2
and Heussler alloys, spin degrees of freedom can be incorporated into
existing FTJs. In such MFTJs, the spin-polarized electrons from a ferromagnetic metallic
electrode tunnel through a ferroelectric thin ﬁlm which serves tunneling barrier. The reversal
of the electric polarization of the ferroelectric ﬁlm leads to a sizable change in the spin
polarization of the tunneling current. This provides a two-state electric control of the spin
polarization, including the possibility of switching from zero to nonzero or from negative to
positive spin polarization and vice versa.
Electrostaticeffect. As is discussed on FTJs, the switching of the electric polarization changes
the potential proﬁle of the whole junction. Then, how does this change affect the conductance
of the minority- and majority-spin carriers? As shown in Fig.11, for the electric polarization
of the FE barrier pointing to the left (i.e., towards the FM electrode), majority-spin carriers
experience an additional barrier compared to minority-spin carriers [compare the solid
and dashed lines in Fig. 11(a)], since the spin dependent potential in FM electrode is
V
σ
1
= V
1
±1/2Δ
ex
, σ is the spin index σ =↓, ↑, Δ
ex
is the exchange splitting strength. This
occurs if the magnitude of the electrostatic potential at the FM/FE interface, ϕ
1
≡ ϕ(0),
is larger than the Fermi energy with respect to the bottom of the minority-spin band, i.e.,
E
F
−V
↓
1
− ϕ
1
< 0. If this condition is met, the spin polarization of the tunneling current is
positive and weakly dependent on the potential barrier height. On the other hand, for the
electric polarization pointing to the right (Fig. 11(b)), i.e., towards the NM electrode, the
tunneling barrier is the same for majority and minority spins [compare the solid and dashed
lines in Fig. 11(b)]. In this case, the magnitude of the spin polarization of the tunneling
current is largely controlled by the exchange splitting of the bands and the potential proﬁle
across the structure. When E
F
− V
↓
1
− ϕ
1
> 0, the asymmetry between R and L is due to
the different barrier transparencies as a result of the different band structures of the two
electrodes. Thus, by reversing the electric polarization of the FE barrier it is possible to switch
the spin polarization of the injected carriers between two different values, thereby providing
a two-state spin-polarization control of the device.
Spin ﬁltering effect. The spin polarization of the conductance can be deﬁned by Π =
G
↑
− G
↓
/G
↑
+ G
↓
, where the conductance can be calculated from Eq. (3). Figs. 12(a) and
25 Ferroelectric and Multiferroic Tunnel Junctions
10 Ferroelectrics
Fig. 11. (Color online) (a) Conductance of a FTJ for two opposite polarization orientations:
Left (solid line) and right (dashed line), as a function of dielectric layer thickness(30). The
insets show the corresponding tunneling barrier proﬁles. (b) TER as the function of dielectric
layer thickness for two polarizations P=20 μC/cm
2
(solid line) and P=40 μC/cm
2
(dashed
line). The inset shows TER as the function of the ferroelectric ﬁlm thickness. U
d
=0.6 eV,
ε
d
=300.
12(b) show the calculated conductance and spin polarization of the conductance as a function
of the potential barrier height, U, in the ferroelectric barrier. It is seen that, for P pointing
towards the ferromagnetic electrode, the spin polarization, Π
L
, is positive and is weakly
dependent on U, reﬂecting an additional tunneling barrier for minority spins (Fig. 11(a)).
On the other hand, for the P pointing towards the NM electrode, the spin polarization, Π
R
,
is slightly negative at not too large values of U and becomes positive when U is larger than
a certain value. The latter result can be understood in terms of spin-dependent tunneling
across a rectangular barrier. Thus, using an appropriate FE barrier, it is possible to change the
spin polarization of injected carriers from positive to negative and vice versa by reversing the
electric polarization of the FE barrier. The degree of the spin polarization change in response
to the electric polarization reversal depends on the carrier density in the semiconductors. This
is illustrated in Fig. 12(c), which shows the dependence of the Π
L
and Π
R
on the Fermi energy
with respect to the bottom of the minority-spin band in the FM electrode. When E
F
≤ V
↓
1
the
DMS is fully spin polarized and hence Π
L
=Π
R
=1. With increasing the carrier concentration
Fig. 12. (Color online)Total conductance, G = G
↑
+ G
↓
(a) and spin polarization (b,c) of
injected current in a FM/FE/NM tunnel junction as a function of potential barrier height
(a,b) and the Fermi energy (c) for the polarization of the ferroelectric barrier pointing to the
left (solid lines) and pointing to the right (dashed lines) for d=3 nm. In (a) and (b) E
F
-V
↑
1
=0.06
eV and V
1
= V
2
; in (c) U=0.5 eV and V
2
−V
↑
1
=0.025 eV(30).
26 Ferroelectrics
Ferroelectric and Multiferroic Tunnel Junctions 11
Fig. 13. (Color online) Tunneling magnetoresistance (a) and conductance, G, for parallel
magnetization of the electrodes (b) in a FM/FE/FM tunnel junction versus potential
difference in the two magnetic semiconductors for the electric polarization of the ferroelectric
barrier pointing to the left (solid lines) and pointing to the right (dashed lines) for d=3 nm
and U=0.5 eV(30).
and hence E
F
, the spin polarization drops down much faster for the P pointing to the right
than for the P pointing to the left, resulting in a sizable difference in the spin polarizations Π
R
and Π
L
. Therefore, by changing the density of carriers in the semiconductors it is possible to
tune values of the spin polarization for a two-state control of the electronic device.
TMR effect. Such multiferroic tunnel junctions (MFTJ) have not yet been realized
experimentally but might be promising in providing an additional degree of freedom in
controlling TMR. Fig. 13(a) shows the calculated TMR in a tunnel junction with two FM
electrodes separated by a FE barrier. The TMR ratio was deﬁned by TMR = G
P
− G
AP
/G
AP
,
where G
P
and G
AP
are the conductances for the parallel and antiparallel magnetization,
respectively. As is seen from Fig. 13(a), for V
1
= V
2
the TMR is independent of the orientation
of P. The increasing potential difference in the two FM electrodes results in the enhancement
of TMR for the P pointing to the right, whereas for the P pointing to the left the TMR drops
down and becomes negative. At these conditions the MFTJ works as a device which allows
switching the TMR between positive and negative values. As follows from Fig. 13(b), there
is a sizable difference in the overall conductance of the junction for the two orientations of
polarization, namely, the TER effect. Therefore, there is a coexistence of TMR and TER effects
in such MFTJs.
3.2 MFTJs with a single-phase multiferroic barrier
Another type of MFTJ is feasible in which the barrier itself is made of a material
that exhibits MF properties in the bulk, such as BiFeO
3
and BiMnO
3
. In multiferroic
materials, the coexistence of ferroelectric and ferromagnetic orders will provide a
unique opportunity for encoding information independently in electric polarization and
magnetization. Consequently, it will open new applications of multiferroic tunnel junctions
on logic programming. Nowadays, several multiferroic tunneling junctions have been
successfully fabricated. For example, Gajek et al. showed that BiMnO
3
tunnel barriers may
serve as spin ﬁlters in magnetic tunnel junctions(32). This work was further advanced to
demonstrate the presence of ferroelectricity in ultrathin BiFeO
3
ﬁlms grown epitaxially on a
half-metallic La
2/3
Sr
1/3
MnO
3
electrode(33)(34) and La
0.1
Bi
0.9
MnO
3
(35).
In this section, two kinds of single-phase MFTJs will be discussed. One is
normal metal/multiferroic/ferromagnetic metal (NM/MF/FM) junction(36). The other is
FM
1
/MF/FM
2
junctions(37), in which both electrodes and the barrier are ferromagnetic. TMR
27 Ferroelectric and Multiferroic Tunnel Junctions
12 Ferroelectrics
Fig. 14. (Color online) Schematic illustration of our multiferroic spin-ﬁlter tunneling
junction, the charge distribution and corresponding electrostatic potential, and the overall
potential proﬁle (from top to bottom)(36). A NM electrode is placed in the left half-space
z <0, a multiferroic barrier of thickness t, and a semiﬁnite FM electrode placed in the the
right half-space z > d. m
L
, m
B
, and m
R
are the effective masses in three regions. μ
L
and μ
R
are the Fermi energies of the left and right electrodes, respectively. Δ
R
and Δ
B
represent the
exchange splitting of the spin-up and spin-down bands in FM electrode and the multiferroic
barrier, respectively. ϕ
L
and ϕ
R
are, respectively, the electrostatic potentials at two interfaces
relative to the Fermi level μ of the system.(a) The electric polarization P points to the right
(positive). (b) P points to the left (negative). Here, it is assumed that two electrodes have
different screening lengths and δ
1
< δ
2
.
and spin ﬁltering effects in these MFTJs are discussed. We also introduce the progress of the
theoretical studies on these single-phase MFTJs.
Structure of NM/MF/FMJunctions. A NM/MF/FMMFTJ is illustrated in Fig.14. Similar to a
FTJ, the screening potential ϕ(z) of a MFTJ is σ
S
δ
L
e
−|x|/δ
L
/ε
L
(x ≤0), and −σ
S
δ
R
e
−|z−t|/δ
R
/ε
R
(x ≥d). Here, δ
L
and δ
R
are the Thomas-Fermi screening lengths in the NMand FMelectrodes,
respectively. ε
L
and ε
R
are the dielectric permittivities of the NM and FM electrodes. The
screening charge σ
S
can be found from the continuity of the electrostatic potential: σ
S
=
(dP/ε
B
)/(δ
L
/ε
L
+δ
R
/ε
R
+d/ε
B
) and ε
B
is the dielectric permittivity of the tunneling barrier.
The overall potential proﬁle is asymmetric, as shown in Fig.14, because it is the sum of the
electrostatic potential ϕ(x), the electronic potential in the electrodes, and the rectangular
potential proﬁle U
0
. Under the applied bias voltage V, the difference of the interfacial barrier
heights is δU = U
L
−U
R
= δϕ + eV, where U
L
= μ + ϕ
L
and U
R
= μ + ϕ
R
−eV.
TMR and Spin ﬁltering effects in NM/MF/FM Junctions. The model Hamiltonian for such
MFTJs can be given by
ˆ
H
σ
= −

(μ
R
+ eV)
2
−Δ
2
R
(8)
which is related with the barrier height ϕ
R↑
induced by electric polarization. Figs. 15 and 16
shows the effect of the barrier’s properties on the spin ﬁltering coefﬁcient and TMR ratio.
Four Logic states. As displayed in Fig. 17 (upper panel), there are overall eight resistive
states with four independent pairs (A, A’; B, B’; C, C’; and D, D’), depending on the relative
orientation of neighboring magnetizations and the sign of P. Because of the magnetoelectric
coupling in the multiferroics, the P and the M can be reversed by an electric ﬁeld separately
or simultaneously. Thus, electric-ﬁeld controlled functionality can be realized, including
normal electroresistance (the transition from A to B or the transition from C to D) and more
signiﬁcant change in resistance, i.e., electromagnetoresistance (the transition from A to D).
The difference between these states is complex but important for practical application. In the
lower panel of Fig. 17, we show the resistance (normalized to its value at P
c
) as a function
of electric polarization, and the inset displays the exchange splitting dependence of P
c
, where
states B and C cross. Compared with conventional TMR elements which have been applied
in magnetic random access memory, and also with FTJs, the present multiferroic structure
possesses both electric controllable switching and large contrast between resistive states.
TMR effect in FM
1
/MF/FM
2
junctions. In the following sections, another kind of MFTJs is
discussed. As shown in Fig. 18, a multiferroic barrier is separated by two ferromagnetic
metallic electrodes, for example, half-metallic La
2/3
Sr
1/3
MnO
3
and ferromagnetic metal
Co(33)(34). Evidently, it is also a kind of magnetic tunnel junction, which will show
Fig. 16. (Color online) (a) The exchange splitting dependence of spin ﬁltering efﬁciency for
different P. δ
L
=0.07 nm and δ
R
=0.08 nm. The inset shows the corresponding TMR. (b) The
same with (a) but with a stronger contrast between δ: δ
L
=0.07 nm and δ
R
=1 nm(36).
30 Ferroelectrics
Ferroelectric and Multiferroic Tunnel Junctions 15
Fig. 17. (Color online) (Upper panel) Schematic illustration of multiple resistive states,
depending on the orientation of P, M and MR. (Lower panel) The electric polarization
dependence of normalized conductance for the four resistive states. δ
L
=0.07 nm, δ
R
=1 nm,
ε
B
=2000, and Δ
B
=0.06 eV. The inset shows the Δ
B
dependence of P
c
(36).
signiﬁcant TMR behaviors. Two theoretical models have been proposed to explain TMR
effects in MTJs. One is Jullieres formula with TMR =
2P
2
1+P
2
(3), where the spin polarization
Fig. 18. (Color online) (a) Schematic illustration of MF tunnel junction. (b) Charge
distribution and corresponding electrostatic potential. (c) The overall potential proﬁle. (d)
Schematic band structures of Co and half-metallic La
2/3
Sr
1/3
MnO
3
(37). The exchange
splittings are Δ
L
, Δ
R
, and Δ
B
, respectively, for the left and right FM electrodes and the MF
barrier. The electric polarization P induces surface charge densities, ±σ
P
= ±|P · x| = P cos α,
on the two surfaces of the barrier, where α is the relative orientation between the electric
polarization P and the x axis. θ
R
= +1(⇑) is ﬁxed, while let θ
B
and θ
L
vary.
31 Ferroelectric and Multiferroic Tunnel Junctions
16 Ferroelectrics
Fig. 19. (Color online) The electric polarization orientation (α) dependence of the TMR from
Eq. (22)(37). The TMR from both Jullieres and Slonczewskis models is α independent. The
parameters used are the same as that used in the calculations in Fig. 20. Here a 5 nm thick
nonmagnetic barrier is adopted.
P = (N
↑
− N
↓
)/(N
↑
+ N
↓
) and N is the density of states at Fermi level. On the other
hand, in the model by Slonczewski(39), the barrier height on the tunneling is considered and
P = [(k
↑
−k
↓
)/(k
↑
+ k
↓
)][(κ
2
−k
↑
k
↓
)/(κ
2
+ k
↑
k
↓
)], where κ =

(2m/¯ h
2
)/(U −E
F
) and U is
the height of barrier. However, in both models of Julliere and Slonczewski, neither the electric
polarization nor the magnetism of the barrier was considered. For MFTJs, Ju et al. extended
the previous TMR models and ﬁrstly pointed out the TMR is a function of the orientation of
the electric polarization (Fig. 19). They also proved that Slonczewskis model is actually a
special case of their model with P=0 (or α =0) and Δ
B
= 0. Their calculations show that the
TMR of MFTJs are strongly inﬂuenced by the orientation of the electric polarization and the
barrier properties, i.e., effective barrier height
¯
U; the exchange splitting of the barrier, Δ
B
; and
the electric polarization in the barrier, P, which is shown in Fig.19 and Fig.20.
Tunneling electroresistance effect (TER). Since both electrodes and barrier are ferromagnetic,
such tunnel electroresistance (TER), TER = G(π)/G(α = 0) , is a little different from that
in FTJs. In Fig. 20(e), we show such TER as for junctions with various barrier thicknesses.
It is found that TER increases with the increase of d and when the magnetization of the
barrier is parallel to the magnetization of right electrode, the presence of weak ferromagnetism
in BiFeO
3
will make TER more signiﬁcant (Fig. 20(f)). However, it is also noted that
TER is almost independent of the magnetic conﬁguration of two electrodes, i.e., parallel or
antiparallel. These TER effects will be studied experimentally by Bea et al.(33)(34).
Converse piezoelectric effect. Converse piezoelectric effect may also have an important
inﬂuence on the tunneling across a multiferroic(40). When the junction is applied with a bias
voltage V, the converse piezoelectric property causes the strain in the barrier, which hence
induces changes in the barrier thickness d, electron effective mass m
B
, and position of the
conduction band edge E
c
. There are (27)
d = d
0
+ d
33
V
m
B
= m
0
B
(1 + μ
33
ΔS
3
)
E
C
= E
0
C
+κ
3
ΔS
3
(9)
where ΔS
3
=d
33
V/d
0
is the lattice strain and d
33
, μ
33
, and κ
3
are, respectively, the out-of-plane
piezoelectric coefﬁcient, strain sensitivity of the effective mass, and relevant deformation
potential of the conduction band in the barrier. d
0
, m
0
B
, and E
0
c
are their values at V = 0.
32 Ferroelectrics
Ferroelectric and Multiferroic Tunnel Junctions 17
If the applied voltage is positive, the barrier thickness d will be compressed and both the
electron effective mass m
B
and barrier height U will increase. Obviously, each of these
strain-induced changes will change the electron tunneling probabilities, and therefore the spin
ﬁltering efﬁciency and TMR ratio (Figs. 21-22).
4. MFTJs with ferromagnet/ferroelectric composite barriers
For practical applications, the single-phase MF barrier junctions are limited by the scarcity
of existing single-phase multiferroics, and none of which combine large and robust electric
and magnetic polarizations at room temperature. It might be a good idea to use a FE/FM
composite barrier to substitute the single-phase MF barrier(41). Such a composite barrier
junction may be thought as an addition of a conventional spin ﬁlter and a FTJ. Here, FM
insulator (FI) barrier acts as a SF generator, and FE barrier acts as a SF adjustor through the
interplay between ferroelectricity and ferromagnetism at the interface. The large SF effect,
the TMR and TER effects, can be achieved in this two-phase composite barrier based tunnel
junction. The eight resistive states with large difference can also be realized.
Electrostatic effect. Figure 23 shows a junction in which a FE/FI composite barrier is
sandwiched by two metallic electrodes(41). The electrostatic potential induced by the electric
polarization in FE layer is obtained, as shown in Fig. 23(b). The overall potential proﬁle
U(x) across the junction is the superposition of the electrostatic potential ϕ(x), the electronic
potential in the electrodes, and the rectangular potential in FE barrier and FI barrier, as shown
in Fig. 23(c).
Fig. 20. (Color online) (a) The orientation of electric polarization α dependence of
conductance. (b) dependence of TMR. (c) The exchange splitting of the barrier Δ
B
vs
conductance. (d) Δ
B
vs TMR. (e) Δ
B
dependence of the normalized conductance
Gα/G(α = 0) with parallel magnetization in two electrodes. (f) Δ
B
dependence of TER with
parallel (P) and antiparallel (AP) magnetizations in two electrodes(37).
33 Ferroelectric and Multiferroic Tunnel Junctions
18 Ferroelectrics
Fig. 21. (left panel)Piezoelectric effect on the SF and (right panel) TER(40) with Δ
B
=0.015 eV,
P=0.5 C/m
2
, κ
3
=-4.5 eV, μ
33
=10, and Δ
L
=Δ
R
=0 eV.
Spin ﬁltering effect, TMR and TER effect. Choosing the nonmagnetic metals (NMs) as two
electrodes, the spin ﬁltering efﬁciency can be deﬁned as α = (G
↑
−G
↓
)/(G
↑
+ G
↓
), while the
TMR is deﬁned by TMR=(G
P
−G
AP
)/(G
P
+ G
AP
) with changing the two metallic electrodes
Fig. 22. (left panel)Piezoelectric effect on the TMR when Δ
B
=0.015 eV, P=0.5 C/m
2
, κ
3
=-4.5
eV, μ
33
=10, and Δ
L
=0.05 eV, and Δ
R
=0.09 eV. (right panel) Inﬂuence of only the (a)
strain-induced barrier thickness change, (b) electron effective mass change, or (c) barrier
height change on TMR. The inset in (a) shows the magniﬁed curve around V=0.12 eV. The
parameters are Δ
B
=0.015 eV, P=0.5 C/m
2
, Δ
L
=0.05 eV, and Δ
R
=0.09 eV(40).
34 Ferroelectrics
Ferroelectric and Multiferroic Tunnel Junctions 19
Fig. 23. (Color online) Schematic illustration of the charge distribution (a), corresponding
electrostatic potential (b), and potential proﬁle in a NM1/FE/ FI/NM2 tunnel junction C(41).
The solid and dashed lines in (b) show the potential for the polarization P in FE barrier
pointing to the left and to the right, respectively. The blue and red lines in FI barrier in (c)
show the potential seen by the spin-down and spin-up electrons, respectively. Here d
1
and d
2
are the thicknesses of the FE and FI barriers, respectively.
from NMs to FMmetals. To calculate TER, the direction of polarization in FE layer is reversed
from pointing to the right to pointing to the left, while the magnetization in FI layer remains
unchanged.
It can be seen from Fig. 24 that the SF and the TMR effect is mainly determined by the
exchange splitting Δ
B
in FI barrier, and is enhanced (reduced) by the polarization in FE
barrier when P points the left (right) electrode. The results here are similar to those for the
single-phase MF barrier junction, indicating that the physical mechanism responsible for SF
effect is the same in both structures, i.e., the ferromagnetismin the barrier, making the barrier
height spin dependent, acts as a SF generator, and the ferroelectricity, changing the proﬁle
of the potential across the junction, acts as a SF adjustor. A large TER effect can be found
in MFTJs with composite barriers. The ferroelectricity in FE layer is the dominant factor to
determine the magnitude of the TER effect.
Eight Logic states. By using one or two FM metal electrodes, eight independent logic states
of tunneling conductance can be realized in such MFTJs. The conductances as a function of
the exchange splitting Δ
B
and the electric polarization P are shown in Fig. 24. For practical
applications, the large contrast between eight states is very important. We ﬁnd that when the
carriers tunneling into the right electrode can be highly spin-polarized, the eight states are
differentiated evidently.
35 Ferroelectric and Multiferroic Tunnel Junctions
20 Ferroelectrics
Fig. 24. (Color online) (a) The exchange splitting dependence of SF with P=0.4 C/m
2
. (b) The
electric polarization dependence of SF with Δ
B
=0.13 eV. In (a) and (b), U
01
=0.5 eV, U
02
=1.1
eV, ε
B1
=2000, ε
B2
=1000, and d
1
=d
2
=2 nm. (c) and (d) show the corresponding TMR(41).
5. Magnetoelectric coupling at ferroelectrics/ferromagnetic metal interfaces
MFTJs have a great potential on the practical applications especially on the multistate
logical elements. Due to the magnetoelectric coupling in MFTJ, it is perspective that the
magnetization can be controled by the applied electric ﬁeld, and vice versa. For single-phase
multiferroic barrier, how the ferromagnetic order and ferroelectric order coupling is still a
unsolved question. Therefore, we switch our attention to the ME coupling of the FM/FE/NM
structures(Fig.26)(42).
Electrostatic effect at Ferromagnetic Metal / Ferroelectrics interfaces. For a FM/FE structure,
when the FE layer is polarized, surface charges are created. These bound charges are
compensated by the screening charge in both FM and NM electrodes. In the FM metal, the
screening charges are spin polarized due to the ferromagnetic exchange interaction. The spin
dependence of screening leads to additional magnetization in the FM electrode as illustrated
in Fig. 26(b). If the density of screening charges is denoted as η and the spin polarization of
screening charges is denoted as ζ, we can directly express the induced magnetization per unit
area as
ΔM =
η
e
ζμ
B
. (10)
As this effect depends on the orientation of the electric polarization in FE, the ME coupling is
expected.
Two simple cases can be considered. (1) In an ideal capacitor where all the surface charges
reside at the metal (FM or NM)/FE interfaces, the density of screening charge η reaches its
maximum value η = P
0
, where P
0
is the spontaneous polarization of the FE. This results in a
large induced magnetization [(P
0
/e)ζμ
B
]. (2) In half metals, there is only one type of carriers
that can provide the screening. If a half metal is chosen to be the FM electrode, the screening
36 Ferroelectrics
Ferroelectric and Multiferroic Tunnel Junctions 21
electrons will be completely spin polarized. In this case, a large induced magnetization is also
expected, ΔM =
η
e
μ
B
.
Induced magnetization from screening charges. For FM/FE/NM junctions (Fig.26(a)), the
additional magnetization, caused by spin-dependent screening(43)(44), will accumulate at
each FM/FE interface. Due to the broken inversion symmetry between the FM/FE and
the NM/FE interfaces, there would be a net additional magnetization in each FM/FE/NM
unit cell, unlike the symmetric structures discussed in the previous work. The addition of
magnetization in this superlattice will result in a large global magnetization. In the case of zero
bias in Fig. 26(c), the local induced magnetization, deﬁned as δM(x) = [δn
↑
(x) −δn
↓
(x)]μ
B
, is
a function of distance fromthe interface x. Here, δn
σ
(x) is the density of the induced screening
charges with spin σ. The total induced magnetization ΔM can be calculated by integrating
δM(x) over the FM layer, and
ΔM =

FM l ayer
δM(x) = −
ηM
0
/e
N
0
+ JN
2
0
− J (M
0
/μ
B
)
2
(11)
where N
0
= N
↑
+ N
↓
is the total density of states, M
0
= (N
↑
− N
↓
)μ
B
can be thought
of as the spontaneous magnetization, ε
0
is the vacuum dielectric constant, J is the
Fig. 25. (up panel) (a)The exchange splitting dependence of TER with P=0.4 C/m
2
. (b) The
electric polarization dependence of TER with Δ
B
=0.13 eV. In (a) and (b), U
01
=0.5 eV, U
02
=1.1
eV, ε
B1
=2000, ε
B2
=1000, and d
1
=d
2
=2 nm. (down panel) (a) The exchange splitting and
electric polarization dependence of tunneling conductances with P=0.4 C/m
2
in (a) and Δ
B
=0.13 eV in (b)(41). In (a) and (b), the rectangular potential in FE barrier and FI barrier is 0.5
eV and 1.1 eV, respectively. ε
B1
=2000, ε
B2
=1000, and d
1
=d
2
=2 nm. The inset in (a) shows the
enlarged part with Δ
B
=0.1 eV. The inset in (b) shows the tunneling conductances with the
polarization in FE barrier pointing to the left.
37 Ferroelectric and Multiferroic Tunnel Junctions
22 Ferroelectrics
Fig. 26. (Color online) (a) Schematic illustration of FM/FE/NM tricomponent superlattice.
(b) The distribution of charges and induced magnetization (green shaded area) calculated by
our theoretical model. A and B are two different choices of the unit cell. The directions of
arrows indicate the motions of positive and negative charges across the boundary of the unit
cell A. (c) Electrostatic potential proﬁle(42) . Here, the following assumptions are made. (1)
The difference in the work function between FM and NM is ignored. (2) To screen the bound
charges in FE, the charges in metal electrodes will accumulate at the FM/FE side, and there is
a depletion at the NM/FE side. In this process, the total amount of charge is conserved;
however, the spin density is not conserved because of the ferromagnetic exchange interaction
in the FM metal.
strength of the ferromagnetic exchange coupling in the FM layer, η is the density of
screening charges, λ
FM(NM)
is the screening length of FM (NM) electrode with λ
FM
=
(e
2
N
0
/ε
0
)[N
0
+ JN
2
0
− J(M
0
/μ
B
)
2
]/(1 + JN
0
)
−1/2
, and t
FM
, t
FE
, and t
NM
are the thicknesses
of FM, FE, and NM layers, respectively. It is seen that the local induced magnetization δM(x)
decays exponentially away from the FM/FE interface.
The induced magnetization in FM/FE/NM tricomponent superlattice with several FM
electrodes, i.e., Fe, Co, Ni, and CrO
2
, are calculated.(42) Detailed parameters and calculated
values of Δ
M
are listed in Fig.27. The magnitude of Δ
M
is found to depend strongly on the
choice of the FM and FE. Among the normal FM metals (Ni, Co, and Fe), the largest Δ
M
is
observed in Ni for its smallest J and highest spontaneous spin polarization M
0
/μ
B
N
0
. On
the other hand, we also predict a large Δ
M
for the 100% spontaneous spin polarization in
half-metallic CrO
2
.
Fig. 27. Calculated induced magnetization(42). Here, ΔM is the value at V
a
=V
C
, where V
a
is
the applied bias and V
C
is the coercive bias.
38 Ferroelectrics
Ferroelectric and Multiferroic Tunnel Junctions 23
Fig. 28. (Color online) Layer-resolved induced magnetic moment of Fe near the interface
between Fe and BaTiO
3
in the Fe/BaTiO
3
/ Pt superlattice(42). Solid line is the ﬁtted
exponential function for the induced moment as a function of the distance from the interface.
First-principle calculations. The ﬁrst-principle calculations are consistent with the results
of the theoretical model. For example, the ﬁrst-principle calculation of the Fe/FE/Pt
superlattice will be shown.(45) The calculations are within the local-density approximation
to density-functional theory and are carried out with VASP. We choose BaTiO
3
(BTO) and
PbTiO
3
(PTO) for the FE layer. Starting from the ferroelectric P4mm phase of BTO and PTO
with polarization pointing along the superlattice stacking direction, we perform a structural
optimization of the multilayer structures by minimizing their total energies. The in-plane
lattice constants are ﬁxed to those of the tetragonal phase of bulk FEs. Figure 19 shows the
calculated induced magnetic moment relative to that of bulk Fe near the Fe/BTO interface
when the polarization in BaTiO
3
points toward the Fe/BTO interface. It is evident that the
induced moments decay exponentially as the distance from the interface increases. This
result is in line with our model for the magnetization accumulation in the FM at the FM/FE
interface. A numerical ﬁtting of the exponential function yields a screening length of 0.7
˚
Afor
the Fe/BaTiO
3
/ Pt structure. This value is comparable to the screening length parameters
calculated using the theoretical model as shown in Fig.28.
Fig. 29. (Color online) ΔM versus V
a
/l for different ferromagnetic metal electrodes. V
a
is the
applied bias and l is the number of the unit cell(42). Here, the thickness of FE layer is 3 nm.
However, a thicker FE layer can be used to avoid the possible electron tunneling effect.
39 Ferroelectric and Multiferroic Tunnel Junctions
24 Ferroelectrics
Electric Control of Magnetization. A natural question is what happens to Δ
M
when
an external bias V is applied. In this case, the electric polarization P will have two
parts: the spontaneous polarization P
0
and the induced polarization. The equation
determining P is obtained by minimizing the free energy. From the continuity of the normal
component of the electric displacement, we ﬁnd equation relating η and P:η = [(Pt
FE
/ε
FE
) +
(V
a
/l)]/[(λ
FM
+ λ
NM
)/ε
0
] + (t
FE
/ε
B
). Here, ε
FE
is the dielectric constant of the FE layer.
These two equations need to be solved self-consistently. The value of η at a given bias can
then be calculated and the induced magnetization ΔM is given by Eq. (11). The free-energy
density F includes contributions from the FE layer, FM layer, and FM/FE interface and takes
the form
F =
t
FE
F(P) + t
FM
F(M) + F
I
(F, M)
t
FE
+ t
FM
+ t
NM
(12)
M is the magnetization of the bulk ferromagnet and here M = M
0
because of zero external
magnetic ﬁeld. The interface energy F
I
(P, M) is the sum of the electrostatic energy and
magnetic exchange energy of the screening charges,
F
I
(F, M) =
(λ
FM
+ λ
NM
)
2ε
0
η
2
+
J
2μ
2
B
(M +ΔM) ΔM (13)
For FE, the free-energy density F(P) can be expressedas F(P) = F
P
+α
P
P
2
+ β
P
P
4
+

P
0
E
B
dP,
where F
P
is the freeenergy density in the unpolarized state. α
P
and β
P
are the usual Landau
parameters of bulk ferroelectric. E
B
is the depolarization ﬁeld in the FE ﬁlm. Similarly, F(M)
can be expanded as a series in the order parameter M, i.e., F(M) = F
M
+ μ
M
M
2
+ ν
M
M
4
,
where F
M
is the free-energy density of bulk ferromagnet and μ
M
and ν
M
are the Landau
parameters of bulk ferromagnet. The calculated induced magnetization as a function of the
applied bias is shown in Fig. 29. Clearly, the electrically controllable magnetization reversal is
realized.
Magnetoelectric coupling energy at the FM/FE interface. To discuss the macroscopic
properties of the electric control of magnetization, we analyze the magnetoelectric coupling
energy in our tricomponent superlattice. For the macroscopic average polarization to be
represented by the electric polarization obtained for a unit cell, this cell needs to be chosen
with special care. Therefore, in the following calculation of total free energy, unit cell B in Fig.
26(b) is chosen, and
¯
P =
Pt
FE
+ η (t
FM
+ t
NM
)
t
FE
+ t
FM
+ t
NM
(14)
The macroscopic average magnetization
¯
M =
Mt
FM
+ΔM
t
FE
+ t
FM
+ t
NM
(15)
Considering the lowest-order termof the magnetoelectric coupling,
¯
P and
¯
M can be expanded
as
¯
P = c
p
P + c

44
2. Photoluminescence in ferroelectric nanopowders and nanowires
2.1 Photoluminescence in ferroelectric nanopowders
Photoluminescence from rare earth ions in ferroelectric nanopowders has been studied by
some research groups. Badr, et al. studied the effect of Eu
3+
contents on the
photoluminescence of nanocrystalline BaTiO
3
powders [11]. The powders were prepared by
sol-gel technique using Ba(Ac)
2
, and Ti(C
4
H
9
O)
4
as raw materials, annealed at 750
o
C in air
for 0.5 h. The crystallite size of the doped sample with 4% Eu
3+
ions in the powder was
found to be equal to 32 nm. The photoluminescence of nanocrystalline powders at 488 nm
were observed. The luminescence spectra of ultra fine Eu
3+
:BaTiO
3
powders are dominated
by the
5
D
0
→
7
F
J
(J=0-4) transitions, indicating a strong distortion of the Eu
3+
sites. The
structure disorder and charge compensation were suggested to be responsible for the strong
inhomogeneous broadening of the
5
D
0
→7F luminescence band of the Eu
3+
.
Fu, et al. studied characterization and luminescent properties of nanocrystalline Pr
3+
-doped
BaTiO
3
powders synthesized by a solvothermal method using barium acetylacetonate
hydrate, titanium (IV) butoxide, and praseodymium acetylacetonate hydrate as precursors
[12]. They discussed the luminescence mechanism, the band gap change and the size
dependence of their fluorescence properties of the powders.
Lemos and coworkers studied up-conversion luminescence properties in Er
3+
/Yb
3+
-codoped
PbTiO
3
perovskite powders prepared by Pechini method [13]. Efficient infrared-to-visible
conversion results in green (about 555 nm) and red (about 655 nm) emissions under 980 nm
laser diode excitation. The main up-conversion mechanism is due to the energy transfer
among Yb and Er ions in excited states.
On the other hand, photoluminescence from defects such as oxygen vacancies or structure
disorder is worth studying. Lin, et al. prepared nanosized Na
0.5
Bi
0.5
TiO
3
powders with
particle size of about 45-85 nm using a sol-gel method and studied their photoluminescence
properties [14]. It was observed from photoluminescence spectra that the main emission
peak of the nanosized powder exhibited a blue shift from 440.2 to 445.3 nm with decreasing
particle size, while the emission intensity increased. They explained that the visible emission
band is due to self-trapped excitation, and this blue shift of the main emission was
attributed to distortion of TiO
6
octahedra originated from the surface stress of Na
0.5
Bi
0.5
TiO
3

(BiT) powders obtained by the complex polymerization method [15]. The BiT powders
annealed at 700
o
C for 2 h under oxygen flow show an orthorhombic structure without
impurity phases. UV-vis spectra indicated that there are intermediary energy levels within
the band gap of the powders annealed at low temperatures. The maximum PL emissions
were observed at about 598 nm, when excited by 488 nm wavelengths. Also, it was observed
that there were two broad PL bands, which were attributed to the intermediary energy
levels arising from alpha-Bi
2
O
3
and BiT phases.
Pizani, et al. reported intense photoluminescence observed at room temperature in highly
disordered (amorphous) BaTiO
3
, PbTiO
3
, and SrTiO
3
prepared by the polymeric precursor
method [16]. The emission band maxima from the three materials are in the visible region
and depend on the exciting wavelength. The authors thought that photoluminescence could
be related to the disordered perovskite structure.
Highly intense violet-blue photoluminescence at room temperature was also observed with
a 350.7 nm excitation line in structurally disordered SrZrO
3
powders by Longo, et al [17].
Photoluminescence in Low-dimensional Oxide Ferroelectric Materials

45
They discuss the role of structural order-disorder that favors the self-trapping of electrons
and charge transference, as well as a model to elucidate the mechanism that triggers
photoluminescence. In this model the wide band model, the most important events occur
before excitation.
They also reported room temperature photoluminescence of Ba
0.8
Ca
0.2
TiO
3
powders
prepared by complex polymerization method [18]. Inherent defects, linked to structural
disorder, facilitate the photoluminescence emission. The photoluminescent emission peak
maximum was around of 533 nm (2.33 eV) for the Ba
0.8
Ca
0.2
TiO
3
. The photoluminescence
process and the band emission energy photon showed dependence of both the structural
order-disorder and the thermal treatment history.
Intense and broad photoluminescence (PL) emission at room temperature was observed on
structurally disordered Ba(Zr
0.25
Ti
0.75
)O
3
(BZT) and Ca(Zr
0.05
Ti
0.95
)O
3
(CZT) powders
synthesized by the polymeric precursor method [19,20]. The theoretical calculations and
experimental measurements of ultraviolet-visible absorption spectroscopy indicate that the
presence of intermediary energy levels in the band gap is favorable for the intense and
broad PL emission at room temperature in disordered BZT and CZT powders. The PL
behavior is probably due the existence of a charge gradient on the disordered structure,
denoted by means of a charge transfer process from [TiO
5
]-[ZrO
6
] or [TiO
6
]-[ZrO
5
] clusters
to [TiO
6
]-[ZrO
6
] clusters.
Similar photoluminescence behavior was also observed in disordered MgTiO
3
and Mn-
doped BaTiO
3
powders [21,22]. The experimental and theoretical results indicated that PL is
related with the degree of disorder in the powders and also suggests the presence of
localized states in the disordered structure.
Blue-green and red photoluminescence (PL) emission in structurally disordered CaTiO
3
:Sm
powders was observed at room temperature with laser excitation at 350.7 nm [23]. The
generation of the broad PL band is related to order-disorder degree in the perovskitelike
structure.
The photoluminescence from SrZrO
3
and SrTiO
3
crystalline, quasi-crystalline, and quasi-
amorphous samples, prepared by the polymeric precursor method, was examined by ab
initio quantum mechanical calculations [24]. It was used in the modeling the structural
model consisting of one pyramidal TiO
5
or ZrO
5
unit piled upon the TiO
6
or ZrO
6
, which are
representative of disordered structures of quasi-crystalline structures such as ST and SZ. In
quasi-crystalline powders, the photoluminescence in the visible region showed different
peak positions and intensities in SZ and ST. The PL emission was linked to distinct
distortions in perovskite lattices and the emission of two colors-violet-blue in SZ and green
in ST-was also examined in the light of favorable structural and electronic conditions. First
principles calculations on the origin of violet-blue and green light photoluminescence
emission in SrZrO
3
and SrTiO
3
perovskites
Ma, et al. studied synthesis and luminescence of undoped and Eu
3+
-activated Aurivillius-
type Bi
3
TiNbO
9
(BTNO) nanophosphors by sol-gel combustion method [25].
Photoluminescence measurements indicated that a broad blue emission was detected for
BTNO nanoparticles, and the characteristic Eu
3+
ions
5
D
0
→
7
F
J
(J=1-4) transitions were
observed for the doped samples. Further investigation illuminates that the Eu
3+
ions
substituted for Bi
3+
ions at A site in the pseudo-perovskite layers. It can be confirmed from
high bright fluorescence image and short decay time that the novel orange-red phosphor
has the potential applications in luminescence devices.
Ferroelectrics

46
2.2 Photoluminescence in ferroelectric nanowires, nanotubes, and nanosheets
Gu, et al. reported characterization of single-crystalline lead titanate nanowires using
photoluminescence spectroscopy, and ultraviolet-visible spectroscopy [26,27]. The
nanowires were synthesized by surfactant-free hydrothermal method at 200
o
C. The
nanowires with uniform diameters of about 12 nm and lengths up to 5 um, exhibit a
tetragonal perovskite structure without impurity phases. A blue emission centered at about
471 nm (2.63 eV) is observed at room temperature. Oxygen vacancies are believed to be
responsible for the luminescence in the PbTiO
3
nanowires.
Chen, et al. prepared ferroelectric PbHPO
4
nanowires by a hydrothermal method at 180 °C
for 24 h using a single-source precursor, Pb(II)−IP6 (IP6, inositol hexakisphosphate acid)
complex [28]. PL measurements indicate that the nanowires exhibit a broad emission peak at
460 nm under the excitation of 375 nm.
Yang et al. reported synthesis of high-aspect-ratio PbTiO
3
nanotube arrays by the
hydrothermal method [29]. The PbTiO
3
nanotube arrays have a tetragonal perovskite
structure without any other impurity phases. A strong green emission band centered at 550
nm (2.25 eV) was observed in PbTiO
3
nanotube arrays at room temperature. Local defects in
PbTiO
3
nanotube arrays were thought to result in the photoluminescence behavior.
PbTiO
3
nanotube arrays have also been synthesized via sol–gel template method. These
nanotubes have a diameter about 300 nm and a length 50 um, with a wall thickness of
typically several tens of nanometers. The as-prepared PTO nanotubes possess
polycrystalline perovskite structure. An intense and wide emission band centered at 505 nm
was observed [30]. The photoluminescence of PTO nanotubes was attributed to the radiative
recombination between trapped electrons and trapped holes in localized tail states due to
structural disorder and gap states due to a large amount of surface defects and oxygen
vacancies.
Ida, et al. successfully prepared layered perovskite SrBi
2
Ta
2
O
9
nanosheets with a thickness of
about 1.3 nm. The nanosheets showed visible blue luminescence under excitation at 285 nm at
room temperature [31]. The luminescence property of the nanosheets was found to be largely
sensitive to the change in the surface environment such as adsorption of H+ and/or OH-.
3. Photoluminescence properties of (Bi, Ln)
4
Ti
3
O
12
thin films
As is known, lanthanide doped bismuth titanate thin films are the most promising
candidate materials for ferroelectric nonvolatile random access memory applications due to
their superior properties such as nonvolatility, long retention time, high fatigue resistance.
Recently, photoluminescence properties originated from some rare earth ions in these kinds
of the thin film materials have attracted much attention for possible integrated
photoluminescent ferroelectric thin film devices.
3.1 Crystal structure of lanthanide doped bismuth titanate thin films
Lanthanide doped bismuth titanate, Bi
4-x
Ln
x
Ti
3
O
12
(BLnT) consists of a layered structure of
(Bi
2
O
2
)
2+
and (Bi
2
Ti
3
O
10
)
2-
pseudo-perovskite layers. Its crystal structure can be formulated
as (Bi
2-x
Ln
x
Ti
3
O
10
)
2-
(Bi
2
O
2
)
2+
, in which three perovskite-like unit cells are sandwiched
between two bismuth oxide layers along the c axis of the pseudotetragonal structure. The
lattice paramenters of Bi
4-x
Ln
x
Ti
3
O
12
(using rare element La as an example) are a=0.542
nm,b=0.541 nm, and c=3.289 nm, respectively. The lanthanide ions substitute for the Bi ions
Photoluminescence in Low-dimensional Oxide Ferroelectric Materials

concentrations (x=0.25, 0.40, 0.55, 0.70, and 0.85, respectively) on the photoluminescence
properties of BEuT thin films indicates that there is an unusual composition quenching
effect of photoluminescence as shown in Fig.3 [36]. The quenching concentration of BEuT
thin films is about 0.40. Similar unusual concentration quenching effect of
Ferroelectrics

48
photoluminescence has also been observed in some Eu
3+
-ion-activated layered perovskite
luminescent powder materials such as Na
2
Gd
2(1-x)
Eu
2x
Ti
3
O
10
, NaGd
1-x
Eu
x
TiO
4
, and RbLa
1-
x
Eu
x
Ta
2
O
7
[43,44]. It was suggested that in these layered perovskite luminescent powder
materials, the energy transfer was restricted in the Eu
3+
sublattices. Similarly, in our case,
BEuT has a bismuth layer perovskite structure, and the Eu
3+
ions in BEuT thin films are
mainly substituting for the Bi
3+
ions in (Bi
2-x
Eu
x
Ti
3
O
10
)
2-
perovskite-like layers rather than in
(Bi
2
O
2
)
2+
layers, therefore, the energy transfer might occur in the nearby Eu
3+
ions in the
perovskite-like layers, thus resulting in the unusual concentration quenching of BEuT thin
films. When the concentration of Eu
3+
ions exceeds the critical value, the radiative centers
increase with increasing doping amount of Eu
3+
ions, however, at the same time the
quenching centers also increase, this would lead to increase of the non-radiative rate,
consequently, the PL intensity decreases.

Fig. 1. Optic transmittance of BEuT (x=0.85) thin films annealed at different temperatures.
From Ref. [36] Ruan, K.B., et al., J. Appl. Phys., 103, 074101 (2008). Copyright American
Institute of Physics (2008)
Electrical measurements indicated that the BEuT thin films also showed ferroelectric
properties comparable to those of BEuT thin films deposited on Pt/Ti/SiO
2
/Si substrates
annealed at the same temperature for 1 h [45]. High fatigue resistance was also observed
after 10
10
switching cycles.
For most BLnT thin films, the doping amount of rare ions about 0.85 results in better
electrical properties of the thin films [4, 46,47]. However, the quenching concentration x of
Bi
4-x
Eu
x
Ti
3
O
12
thin films is about 0.40, which is much lower than 0.85. In order to obtain the
BLnT thin films with both good electrical and photoluminescent properties at the same time,
we proposed to prepare Eu- and Gd- codoped bismuth titanate (Bi
3.15
Eu
0.425
Gd
0.425
Ti
3
O
12
,
BEGT) thin films with both Eu
3+
and Gd
3+
doping amounts being 0.425, giving a total
doping amount of rare earth ions of 0.85. It was expected that, on the one hand, the BEGT
thin films might exhibit good photoluminescent properties since Eu
3+
doping amount of
0.425 in the thin films is close to the quenching concentration about 0.40 of BEuT thin films,
on the other hand, the BEGT thin films might also show good electrical properties
comparable to those of BEuT thin films and of BGdT thin films because total doping amount
of rare earth ions is maintained to be 0.85 in the thin films. Figure 7 shows the emission
Photoluminescence in Low-dimensional Oxide Ferroelectric Materials

49
spectra of BEGT and BEuT thin films under 350 nm exciting wavelength [37]. The
enhancement of emission intensities for two Eu
3+
emission transitions of
5
D
0
→
7
F
1
(594 nm)
and
5
D
0
→
7
F
2
(617 nm) was observed for the BEGT thin films as compared to BEuT thin
films. This photoluminescence improvement can be attributed to Eu content of BEGT thin
films close to quenching concentration of BEuT thin films and local distortion of crystal field
surrounding the Eu
3+
activator induced by different ionic radii of Eu
3+
and Gd
3+
ions. As
mentioned before, the critical value of quenching concentration for Bi
4-x
Eu
x
Ti
3
O
12
thin films
was near x=0.40. In the case of BEGT thin films, Eu
3+
doping amount of 0.425 is close to the
quenching concentration 0.40 of BEuT thin films, therefore, BEGT thin films exhibit better
photoluminescence than Bi
3.15
Eu
0.85
Ti
3
O
12
thin films. In addition, local distortion of crystal
field surrounding the Eu
3+
activator induced by different ionic radii of Eu
3+
and Gd
3+
ions in
BEGT thin films also contributes to the enhancement of photoluminescence.

Fig. 2. Excitation and emission spectra of BEuT (x=0.85) thin films annealed at different
temperatures. From Ref. [36] Ruan, K.B., et al., J. Appl. Phys., 103, 074101 (2008). Copyright
American Institute of Physics (2008)
In addition, the BEGT thin films had larger remanent polarization and higher dielectric
constant than BGdT and BEuT thin films prepared under the same experimental conditions.
Therefore, co-doping of rare earth ions such as Eu and Gd in bismuth titanate thin films is
an effective way to improve photoluminescence and electrical properties of the thin films.
As mentioned before, the bismuth layered perovskite structure BLnT exhibits strong
structural anisotropy, which results in strong crystallographic orientation dependence of
ferroelectric properties. Many studies indicate that c-axis-oriented (001) epitaxial
(Bi,La)
4
Ti
3
O
12
, (Bi,Nd)
4
Ti
3
O
12
thin films exhibit a very low remanent polarization along the
film normal, because the vector of the spontaneous polarization in the layered perovskite
materials is almost along a axis. Therefore, it is of interest to know whether there is similar
orientation dependence of PL properties of BEuT thin films [48].
Ferroelectrics

51
concentration of x=0.55. It is worth noting that the quenching concentration of BEuT thin
films prepared on STO (100) substrates is higher than that (x=0.4) for the thin films on ITO-
coated glass. This may be ascribed to effects of the crystal orientation of BEuT thin films. The
BEuT thin films prepared on STO (100) substrates show high c axis orientation, while BEuT
thin films on ITO-coated glass and quartz substrates exhibit random orientation. For
randomly oriented thin films, more non-radiative defects existed in the grain boundaries,
resulting in decrease of quenching concentration.

52
Figure 6 shows the PL emission spectra of Bi
3.45
Eu
0.55
Ti
3
O
12
thin films prepared on STO (100)
and STO (111) substrates [48]. It can be observed that the emission intensity of BEuT thin
films on STO (100) substrate is obviously stronger than that on STO (111) substrate. On the
one hand, the orientation difference of the thin films might affect PL properties of BEuT thin
films, specifically, well-aligned grains with c-axis oriented growth lead to low light
scattering; on the other hand, the surface roughness may also affect detection of PL
properties of thin film materials. It has been reported that rougher surfaces of
photoluminescent thin films reduce internal reflections [49]. However, our AFM observation
showed that the root mean square roughness values of both the BEuT thin films on the two
different substrates are close (15.2 nm on STO (100) substrate and 13.8 nm on STO (111)
substrate, respectively). This implies that different PL properties are mainly caused by the
orientation difference of BEuT thin films. Note that different from orientation dependence of
ferroelectric properties of the rare earth doped bismuth titanate thin films, the c-axis
oriented BEuT thin films on STO (100) substrates exhibited stronger photoluminescence
than the randomly oriented thin films on STO (111) substrates.
3.3 Nanocomposite films composed of ferroelectric Bi
3.6
Eu
0.4
Ti
3
O
12
matrix and highly
c-axis oriented ZnO nanorods
PL properties of BEuT thin films might have potential applications for integrated
photoluminescent ferroelectric thin film devices. However, further enhancement of emission
intensity of BEuT is desirable. For this purpose, Zhou, et al. developed a hybrid chemical
solution method to prepare nanocomposite films composed of ferroelectric BEuT matrix and
highly c-axis oriented ZnO nanorods with an attempt to achieve a more efficient energy
transfer from ZnO nanorods to Eu
3+
ions in BEuT, and thus, to enhance the PL intensity of
BEuT [50].
Figure 7 shows emission spectra of (a) the nanocomposite film composed of BEuT matrix
and highly c-axis oriented ZnO nanorods and (b) the BEuT thin film [50]. The excitation
wavelength is chosen as 350 nm, as the internal band excitation is more efficient than the
intrinsic excitation of Eu
3+
in BEuT host. Compared with individual BEuT thin film, the
nanocomposite film of BEuT matrix and ZnO nanorods exhibits much more intense
emissions centered at 594 nm and 617 nm from Eu
3+
ions. The emission intensities are about
10 times stronger than those for individual BEuT thin film. At the same time, in the emission
spectrum, a sharp UV emission at about 380 nm and a broad band emission centered at 525
nm are also observed. The former can be attributed to near band edge emission of ZnO, and
the latter is commonly believed to originate from defect-related deep-level emission in ZnO,
such as the radiative recombination of photo-generated holes with electrons occupying the
oxygen vacancies.
By comparing the emission spectrum of the nanocomposite film composed of BEuT matrix
and highly c-axis oriented ZnO nanorods and excitation spectrum of the BEuT thin film, it
was found that there are two spectral overlaps between the emission bands of ZnO
nanorods and the absorption bands of Eu
3+
ions in BEuT. One is located between sharp UV
emission at 380 nm of ZnO and transition of
7
F
0
→
5
L
6
at 395 nm of Eu
3+
ions, and the other
one is between defect-related deep-level emission band centered at 525 nm of ZnO and
transition of
7
F
0
→
5
D
2
at 465 nm of Eu
3+
ions. It has been believed that energy transfer occurs
only when the emission band of sensitizer (ZnO in this study) overlaps spectrally with the
absorption band of activator (Eu
3+
ions in this study). In our case, under the excitation of 350
Photoluminescence in Low-dimensional Oxide Ferroelectric Materials

53
nm radiation, ZnO nanorods firstly absorb the radiation energy, and promote electrons to
move from the valence band to the conduction band, leading to band edge emission of ZnO.
Then, due to the spectral overlap between the band edge emission of ZnO nanorods and the
7
F
0
→
5
L
6
excitation spectrum of Eu
3+
ions centered at 395 nm in BEuT, an efficient energy
transfer from the ZnO nanorods to Eu
3+
ions occurs, promoting the Eu
3+
ions from
7
F
0

ground state to
5
L
6
excited state [51]. The Eu
3+
ions in the excited state
5
L
6
undergo
nonradiative decay to the
5
D
0
state because the gaps of adjacent levels are small. Then,
radiative transition takes place between the
5
D
0
and the
7
F
J
(J=0–6) states because of the
larger gap [52,53]. This is one of the reasons that red PL of Eu
3+
ions can be enhanced.
On the other hand, the defect states such as oxygen vacancies in the ZnO nanorods also
capture electrons, and generate a broad band green emission centered at 525 nm. Due to the
spectral overlap between the defect-related emission of ZnO and the absorption band of
7
F
0
→
5
D
2
transition at 465 nm of Eu
3+
ions, an efficient energy transfer also occurs. Thus,
some Eu
3+
ions are promoted from the ground state
7
F
0
to the excited state
5
D
2
. Similarly,
this can also result in enhancement of red PL of Eu
3+
ions. It has been reported that the
defect states (trapping centers) in ZnO can temporarily store the excitation energy, then
giving rise to efficient energy transfer from the traps in ZnO to Eu
3+
ions [53].
For nonradiative energy transfer, the distance between the emission and absorption centers
must be very close [51]. Therefore, in Eu
3+
-doped ZnO materials the energy transfer is
nonradiative energy transfer [54,55]. However, in our nanocomposite films, the energy
transfer should be a radiative energy transfer because the BEuT matrix can only contact with
the outside part of the ZnO nanorods. It has been reported that in some other materials with
Eu
3+
as activators combined with ZnO quantum dots or ZnO thin films the energy transfer is
radiative energy transfer [51, 56].

54
3.4 (Bi, Pr)
4
Ti
3
O
12
luminescent ferroelectric thin films
Recently, Pr doped ATiO
3
(A=Sr, Ca) titanate thin films have been widely studied for
photoluminescence applications. Usually these thin films exhibit three emission peaks,
which are located at 493 nm, 533 nm, and 612 nm, respectively [57]. Of them, the strongest
peak is at about 612 nm. It is known that the lattice distortion of host materials and/or site
symmetry of rare ions greatly affect the photoluminescence properties. Since Pr doped
SrTiO
3
or CaTiO
3
thin films have simple perovskite structure, whereas Pr
3+
-doped BIT (BPT)
presents bismuth layered perovskite structure, and correspondingly, site symmetry of Pr
ions is different, Pr
3+
-doped BIT thin films are expected to show different photoluminescent
properties. Our study confirmed that BPT thin films also exhibit three emission peaks, at 493
nm, 533 nm, and 612 nm, respectively, however, strongest peak is at 493 nm when Pr doping
content is large than 0.01. It was observed that the Bi
3.91
Pr
0.09
Ti
3
O
12
thin films have highest
photoluminescence intensity, in other words, the quenching concentration for 493 nm
emission is 0.09. Note that the doping amount of Pr
3+
ions was so small that the ferroelectric
properties of BPT thin films were not good. Taking into consideration that lanthanum doped
BIT thin films exhibited good electrical properties, such as relatively high remanent
polarization, low processing temperature, and good polarization fatigue-free properties, and
that La
3+
are usually used as host ions in rare earth luminescence materials because La
3+
ions
do not absorb ultraviolet emission, therefore, La
3+
ions were selected to incorporate into
Bi
3.91
Pr
0.09
Ti
3
O
12
thin films in order to improve the photoluminescence and electrical
properties of the thin films. The results confirmed that both the photoluminescence and
ferroelectric polarization of BPT thin films have been enhanced by La
3+
doping [58].

55
ion content is 0.09, the blue-green emission reaches maximum, indicating that the quenching
concentration of the blue-green emission is 0.09. We note that the red emission (612 nm) has
been relatively weak for all Pr doping contents except Pr doping content of 0.01. This is very
different from that of Pr
3+
doped SrTiO
3
and CaTiO
3
thin films in which the red emission is
strongest whereas the blue-green emission is very weak [59,60]. This is because the
photoluminescence properties of Pr
3+
are sensitive to host lattice symmetry. There is obvious
difference of host lattice between Pr doped titanate with simple perovskite structure and
BPLT with bismuth layered perovskite structure. It has been reported that, in Pr
3+
doped
CaSnO
3
perovskite with an orthorhombic symmetry, the emission from
3
P
0
to
3
H
4
(blue-
green) is dominant over
1
D
2
to
3
H
4
red emission [61]. Okumura and coworkers confirmed
that the
3
P
0
→
3
H
4
transition (blue-green) in R
2
O
3
:Pr
3+
(R=Y, La and Gd) became dominant
instead of
1
D
2
→
3
H
4
transition (red) when the crystal structure was distorted from cubic to
monoclinic [62]. Besides the difference of their crystal structures, local structure or site
symmetry of Pr ions should have a large influence on photoluminescence properties.
As is known, BIT layered perovskite has a monoclinic symmetry below Tc, but it can be
represented as orthorhombic with the c-axis perpendicular to the (Bi
2
O
2
)
2+
layers. In BIT, a
perovskite-like (Bi
2
Ti
3
O
10
)
2−
layer consists of three layers of TiO
6
octahedra, where Bi ions
occupy the spaces in the framework of TiO
6
octahedra, and rare earth ions only substituted
Bi
3+
ions at (Bi
2
Ti
3
O
10
)
2-
perovskite layers. Owing to different lattice structures of BPT from
ATiO
3
(A=Sr, Ca), BPT exhibits different photoluminescent properties. Since the transition
from
3
P
0
to
3
H
4
is spin-allowed, it is understandable that the blue-green emission is
dominant in the BPT thin films.
In order to improve the photolumincesence and ferroelectric properties, we fixed the Pr
content at 0.09, and then added different content La ions into PBT thin films. Figure 9 shows
photoluminescence spectra of BPLT-x thin films with various La contents [58]. Under the
350 nm UV excitation, the BPLT-x thin films also exhibit a strong blue-green emission peak
at 493 nm, together with the other two weaker emission peaks at 533 nm and 612 nm,
respectively. As can be seen, the peaks of emission spectra are similar for all the thin films,
but their emission intensities vary with the La content. When La content x is 0.36, the
emission reaches maximum.

56
To understand the photoluminescence process in BPLT thin films excited under UV light,
the excitation spectra by monitoring the emission at 493 nm and the transmission spectra of
BPLT thin films were measured as shown in Fig.10 [58]. From Fig. 10 (a), it was observed
that Pr doping or Pr-La codoping does not obviously influence the absorption spectra except
the intensity of the broad band at around 350 nm. Meanwhile, the transmission spectra
indicate that all the thin films with different La doping contents show a sharp absorption
edge at around 350 nm as shown in Fig. 10 (b). The results showed that there is good
agreement between excitation peak and absorption edge. This implies the possibility that
the excitation energy from a UV light is first absorbed by the host lattice through the
interband transition, and then the absorbed energy transfers from the host lattice to the
activator Pr
3+
ions.

substitution raised Pr value of the BPT thin film from 6.9 to 19.8 μC/cm
2
, and, at the same
time, reduced the Ec value.
The polarization enhancement by La
3+
substitution can be attributed to crystallization
improvement of the thin films which has been confirmed by XRD and SEM. In addition,
better crystallinity can also result in strong photoluminescence due to higher oscillating
strengths for the optical transitions [41].
Photoluminescence in Low-dimensional Oxide Ferroelectric Materials

57
3.5 (Bi, Er)
4
Ti
3
O
12
luminescent ferroelectric thin films
As described before, BiT doped with Eu
3+
or Pr
3+
ions showed photoluminescence
properties. However, they are only frequency down-conversion photoluminescence, up-
conversion photoluminescence in BiT based thin films is also worth studying.
As is known, Er
3+
/Yb
3+
co-doped materials have been recognized as one of the most
efficient systems for obtaining frequency up-conversion photoluminescence due to the
efficient energy transfer from Yb
3+
to Er
3+
ions pumped by 980 nm [63,64], in which Er
3+
ions
acted as luminescence centers and Yb
3+
ions as sensitizers. On the other hand, considering
the lattice structure of BiT, Er
3+
/Yb
3+
ions can be accommodated in well defined sites of BiT
lattice by substituting for Bi
3+
ions without the need of charge compensation. Therefore, it is
of much interest to study up-conversion luminescence properties of Er
3+
/Yb
3+
co-doped BiT
thin films [65].
Figure 11 shows the up-conversion luminescence spectra for the BErT and BYET thin films
under a 980 nm laser excitation at room temperature [65]. As can be seen from Fig.11, there
are three distinct up-conversion emission bands, of which the two bands centered at 524 nm
and 545 nm, correspond to strong green light emissions ascribed to
2
H
11/2
to
4
I
15/2
and
4
S
3/2

to
4
I
15/2
transitions of Er
3+
ions, respectively, and another band centered at 667 nm to very
weak red light emission originated from
4
F
9/2
to
4
I
15/2
transition of Er
3+
ions. The green
emission at 549 nm is 20 times as strong as the red emission at 667 nm. Meanwhile, BYET
thin films exhibit higher green emission intensity by a factor of about 30 compared with
BErT thin films. It is worth noting that the near pure green up conversion
photoluminescence is bright enough to be clearly observed by the naked eyes. This indicates
that the up-conversion photoluminescence efficiency of BiT thin films co-doped by Er
3+
and
Yb
3+
has been greatly improved.

polycrystalline thin films prepared by same method [73]. The thin films also show strong
red luminescence. It was found that the substrate properties such as optical absorbance and
thermal conductivity affected the crystal growth and the PL emission of the thin films in the
excimer laser assisted metal organic deposition process.
Takashima, et al. observed intense red photoluminescence under ultraviolet excitation in
epitaxial Pr-doped Ca
0.6
Sr
0.4
TiO
3
perovskite thin films prepared on SrTiO
3
(100) substrates
by pulsed laser deposition [74]. The observed sharp PL peak centered at 610 nm was
assigned to the transition of Pr
3+
ions from the
1
D
2
state to the
3
H
4
state. It was suggested
that the UV energy absorbed by the host lattice was transferred to the Pr ions, leading to the
red luminescence.
Rho, et al. prepared SrTiO
3
thin films by rf-sputtering and studied the photoluminescence of
the thin films after postannealing treatments [75]. The remarkable room temperature PL
effects observed are contributed to both metastable and energetically stabilized defect states
formed inside the band gap.
Moreira, et al. [76] studied photoluminescence of barium titanate and barium zirconate in
multilayer disordered thin films at room temperature. The thin films were prepared by spin-
coating and annealed at 350, 450, and 550
o
C for 2 h. It was observed that the wide band
Photoluminescence in Low-dimensional Oxide Ferroelectric Materials

Lim, S. F., Riehn, R., Ryu, W. S., Khanarian, N., Tung, C. K., Tank, D. & Austin, R. H.
(2006) Nano Lett., 6, 169.
[65] Gao, F., Wu, G.H., Zhou, H. & Bao, D.H. (2009) J. Appl. Phys., 106, 126104.
[66] Reshmi, R., Jayaraj, M. K., Jithesh, K., Sebastian, M. T. (2010) J. Electrochem. Soc., 157 (7):
H783-H786.
[67] Kuo, S.Y., Hsieh, W.F. (2005) J. Vac. Sci. & Technol. A , 23 (4): 768-772.
[68] Garcia Hernandez, M., Carrillo Romo, F. de J., Garcia Murillo, A., Jaramillo Vigueras,
D., Meneses Nava, M. A., Bartolo Perez, P., Chadeyron, G. (2010) J. Sol-Gel Sci. &
Technol., 53 (2): 246-254.
[69] Aizawa, K., Ohtani, Y. (2007) Jpn. J. Appl. Phys. Part 1, 46 (10B): 6944-6947.
[70] Aizawa, K., Ohtani, Y. (2008) Jpn. J. Appl. Phys. Part 2, 47 (9): 7549-7552.
[71] Nakajima, T., Tsuchiya, T., Kumagai, T. (2008) Curr. Appl. Phys., 8 (3-4): 404-407.
[72] Yamamoto, H., Okamoto, S., Kobayashi, H. (2002) J. Lumin., 100 (1-4): 325-332.
[73] Nakajima, T., Tsuchiya, T., Kumagai, T. (2007) Appl. Surf. Sci., 254 (4): 884-887.
[74] Takashima, H., Ueda, K., Itoh, M. (2006) Appl. Phys. Lett., 89 (26): 261915.
[75] Rho, J., Jang, S., Ko, Y.D., Kang, S., Kim, D.W., Chung, J.S., Kim, M., Han, M., Choi,
E. (2009) Appl. Phys. Lett., 95 (24): 241906.
[76] Moreira, M. L., Gurgel, M. F. C., Mambrini, G. P., Leite, E. R., Pizani, P. S., Varela, J. A.,
Longo, E. (2008) J. Phys. Chem. A, 112 (38): 8938-8942 .
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Pizani, P. S., Longo, E. (2007) Acta Mater. A, 55 (19): 6416-6426.
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0
Optical Properties and Electronic Band Structures
of Perovskite-Type Ferroelectric and Conductive
Metallic Oxide Films
Zhigao Hu
1
, Yawei Li
1
, Wenwu Li
1
, Jiajun Zhu
1
,
Min Zhu
2
, Ziqiang Zhu
3
and Junhao Chu
3
1
Key Laboratory of Polar Materials and Devices, Ministry of Education,
Department of Electronic Engineering, East China Normal University, Shanghai 200241
2
Department of Physics, Shanghai Jiao Tong University, Shanghai 200240
3
Key Laboratory of Polar Materials and Devices, Ministry of Education,
Department of Electronic Engineering, East China Normal University, Shanghai 200241
People’s Republic of China
1. Introduction
Ferroelectric (FE) materials have recently attracted considerable attention and intensive
research due to their unique advantages in nonvolatile random-access memories, electro-optic
devices, pyroelectric detectors, and optical mixers. (1; 2; 3; 4; 5; 6) It is well known that FE
ﬁlms can be deposited directly on diversiﬁed substrates and are expected to yield better
sensitivity and faster response than the equivalent bulk single crystal. Nevertheless, the
physical properties of FE ﬁlms are strongly sensitive to the experimental conditions containing
substrate, growth technique, crystalline quality, intrinsic defects, and doping elements,
etc. Hence, it is signiﬁcant to systematically investigate the physical properties of FE ﬁlm
materials, such as optical, electrical, and magnetic properties and their interactions. Among
them, perovskite-type FE materials are the most promising compounds due to the polarization
from the oxygen octahedra. Although there are lots of electrical properties reported on the FE
bulk and ﬁlm materials, optical and electronic properties are still scarce for their applications
in the optoelectronic ﬁeld. As we know, Bi
4
Ti
3
O
12
(BiT) is a very promising compound as a
candidate of FE materials for integrated optics applications due to their combination of low
processing temperatures, fatigue-free properties, high Curie temperature (T
c
∼675
◦
C) and
large spontaneous polarization (P
s
∼50 μC/cm
2
along the a axis). (7; 8) Moreover, it was
reported that the FE and optical properties of BiT materials can be evidently improved by
the La doping, such as Bi
3.25
La
0.75
Ti
3
O
12
(BLT). (9; 10; 11; 12) For Bi-site substitution, the
coercive ﬁeld usually becomes larger than that of pure BiT, while for Ti-site substitution,
the coercive ﬁeld becomes smaller. Theoretical calculation indicates that the La substitution
strikingly decreases the T
c
to about 400
◦
C. (13) Thus, BLT material can be widely accepted for
an interesting compound in some optoelectronic applications owing to a lower T
c
and larger
coercive ﬁeld.
Generally, the phase transitions of perovskite-based oxides represent a basilic class of
structural phase transition that bear signiﬁcant technological implications. (14) The high
4
2 Ferroelectrics
FE phase transition temperature will be valuable for the electronic and optoelectronic
device applications, which can be controlled at room temperature (RT). As we know, the
phase transition of most FE materials can be derived by the soft mode, which can be
studied by Raman scattering and/or far-infrared spectroscopy. (15; 16) Note that the
ferroelectric-paraelectric phase transition of FE materials have been widely investigated to
clarify the T
c
with the aid of electrical measurements, such as the remnant polarization
variations. However, there are some other structural transitions in FE materials except for
the T
c
temperature, which are also crucial to the polarization. (17; 18; 19) It can be expected
that the physical properties of FE compounds, such as dielectric constants and loss tangent
could be changed due to the structure variations at phase transition point. Therefore, the
investigations on the optical properties during the phase transitions are necessary to further
clarify its FE derivation and polarization.
For BiT nanocrystals and ceramics, some experimental results reveal a possible structural
transformation at lower temperatures. (20; 21) Structural transitions are usually studied
by various experimental techniques such as x-ray diffraction (XRD) and Raman scattering.
(22; 23; 24) Although both of the two methods can provide the most direct information about
the phase transitions, the variations of the optical band gap, optical constants, and band tail
state behavior during phase transitions could not be derived due to the intrinsic technique
limitations. Fortunately, far-infrared spectroscopy is commonly applied to observe the
variation of soft mode and dielectric function during the phase transition. (15) Nevertheless,
the band gap behavior and interband electronic transition are still keep as an open issue
because of the wide-band-gap characteristics for most FE materials, which are located in
the ultraviolet photon energy region. Therefore, current attention is focused on ﬁnding a
new method to give more information about the phase transitions, especially for the band
gap region. Motivated by the lack of experimental data about the dielectric functions and
phase transitions for BLT ﬁlm, here we focus on the optical properties of BLT nanocrystalline
ﬁlm with different temperatures to gain a more intensive understanding of the microscopic
mechanism of phase transitions and novel physics in these materials.
On the other hand, top and bottom electrodes play an important role in optoelectronic devices
in order to deal with electrical and/or optical signal. (25; 26; 27; 28; 29) For example,
polarization charges, which can be screened by free carriers inside the electrode, are induced
at the electrode/FE interface in a FE-based capacitor. As we know, LaNiO
3
(LNO) and
La
0.5
Sr
0.5
CoO
3
(LSCO), which are the highly conductive metallic oxides, have a distorted
perovskite structure with a cubic lattice parameter of 3.84 and 3.83
˚
A, respectively. (30; 31; 32)
As the matched electrodes for perovskite FE-based devices, LNO and LSCO materials have
been widely studied as alternatives for platinum (Pt) and Pt-based metals. (26; 29; 33) It is
because these metallic oxides can signiﬁcantly improve the physical properties of FE devices,
as compared with noble metal electrodes. (33; 34) Therefore, understanding the intrinsic
physical phenomena occurring within FE ﬁlm and electrode/FE interface requires accurate
knowledge of dielectric constants about the electrode. Owing to an increasing interest of
nanostructured FE materials and devices, (35; 36) the physical properties of nanostructured
electrodes should be further investigated in order to clarify the functionalities. In spite of the
promising properties up to now, (27; 32; 29) there are no reports on dielectric function and
optical conductivity of nanostructured LNO and LSCO materials, which can predicatively
reﬂect the electrical transport properties and electronic band structure. (37; 38) It is well
known that macroscopical dielectric function and/or optical conductivity can be directly
related to the electronic band structure. (39) In particular, the optical and electronic properties
64 Ferroelectrics
Optical Properties and Electronic Band Structures
of Perovskite-Type Ferroelectric and Conductive Metallic Oxide Films 3
could be remarkably different from the bulk crystal for LNO and LSCO materials with a
low-dimensional structure. (38) Therefore, it is necessary to clarify the optical response
behaviors of the nanostructured oxides.
Fortunately, optical transmittance, reﬂectance, and spectroscopic ellipsometrytechniques, whi
ch are the nondestructive and powerful technique to investigate the optical characteristics
of materials, can directly provide electronic band energy and dielectric constants, etc.
(40; 41; 42; 43) With the aid of the reasonable dielectric function model, one can reproduce the
experimental spectra well and the dielectric functions can be easily extracted. (44) This makes
it possible to investigate the optical properties of wide band gap FE ﬁlms and conductive
metallic oxide ﬁlms in a wider photon energy range. In particular, Spectroscopic ellipsometry,
which is very sensitive to ultrathin ﬁlms and surfaces, is a nondestructive and powerful
technique to investigate the optical characteristics of materials, and, in particular, to measure
the thickness and the dielectric function of a multilayer system simultaneously. (44; 45; 46;
47; 48; 49) As compared to the traditional reﬂectance and/or transmittance spectroscopy,
spectroscopic ellipsometry can determine exactly the ratio of linearly p- and s-polarized
light intensity and the phase difference between p- and s-polarized light simultaneously.
Therefore, spectroscopic ellipsometry can directly provide the optical constants of materials
without Kramers-Kr¨ onig (K-K) analysis. (49; 50) The purpose of the present work is to point
out that spectral technique is an effective tool to study the structural properties and phase
transitions in FE materials and interband transitions in conductive metallic oxides. The results
open a new vista for the experimental technique development of observing phase/structural
transitions. Moreover, it indicates that the spectral techniques can be applied to study the
optical response behavior of perovskite-type FE and conductive metallic oxides.
This chapter is arranged in the following way. In Sec. 2, the detailed growth processes of the
BLT, LNO, and LSCO ﬁlms and spectral setup are described; In Sec. 3, the crystal structures
of the BLT, LNO and LSCO ﬁlms have been presented; In Sec. 4, spectral transmittance,
reﬂectance and ellipsometric theory is expressed; In Sec. 5, optical properties and phase
transition characteristics of the BLT ﬁlms have been discussed. In Sec. 6, the electronic band
structures of the LNO and LSCO ﬁlms on Si substrate are derived in detail; In Sec. 7, the
thickness dependence of infrared optical constants in the LNO ﬁlms on platinized silicon
substrates (Pt/Ti/SiO
2
/Si) is presented; In Sec. 8, the main results are summarized.
2. Experimental
2.1 The fabrications of BLT ﬁlms
The BLT nanocrystalline ﬁlm was prepared on quartz substrate by chemical solution
deposition technique. Bismuth nitrate, lanthanum acetate, and titanium butoxide were
used as starting materials. The BLT precursor solution with a stoichiometric molar ratio of
Bi/La/Ti=3.25/0.75/3 was dissolved in heated glacial acetic acid instead of drastic toxicity
2-methoxyethanol, which makes the process of preparation of precursor solutions safer and
simpler. Note that excess 8 mol% Bi precursor was added to compensate for Bi evaporation
during the annealing process. Then an appropriate amount of acetylacetone was added to
the solution as a stabilizing agent. Equimolar amounts of titanium butoxide were also added
into solution. The concentration of the precursor solution was 0.05 M. In order to improve
the hydrolysis and polymerization, the precursor solution was placed at atmosphere about
10 days before spin coating onto the substrate. The homogeneity and stability of the coating
solution was greatly improved by the addition of acetylacetone. The BLT nanocrystalline
ﬁlm was deposited by spin coating of the solution onto quartz substrate at 3500 rpm for 30
65
Optical Properties and Electronic Band Structures of
Perovskite-Type Ferroelectric and Conductive Metallic Oxide Films
4 Ferroelectrics
s. Each layer was dried at 180
◦
C for 3 min, then calcined at 350
◦
C for 3 min. Finally, the
samples were annealed at 675
◦
C for 3 min by rapid thermal annealing. By repeating the
coating/calcining cycles about ﬁve times, the BLT ﬁlm with the nominal thickness of about
150 nm can be obtained.
2.2 The growths of conductive metallic oxides
Nanocrystalline LNO and LSCO ﬁlms were deposited on the single-side polished silicon (Si)
wafers by radio frequency magnetron sputtering (RFMS) and pulsed laser deposition (PLD)
methods, respectively. A 100-mm-diam LNO target was used for deposition. The distance
between the target and Si(111) substrates was 70 mm. Before deposition, the target was
pre-sputtered for 30 min with the substrate shutter closed to achieve stable conditions. The
vacuum chamber pumped by a turbomolecular pump produceda base pressure of 2 ×10
−4
Pa
and was raised to 1.6 Pa by admitting argon (Ar) and oxygen (O
2
). The Si(111) substrates were
mounted with silver paste onto a resistively heated substrate holder. During the sputtering,
the temperature of the substrate holder was kept at 265
◦
C and the radio frequency power on
the target was 80 W, operating at 13.56 MHz, yielding a growth rate of about 2-3 nm/min.
After deposition, a cooling was carried out in vacuum. Following with the above method, the
LNO ﬁlm with the nominal thickness of about 230 nm can be derived.
For the LSCO ﬁlm, however, a KrF excimer laser with the pulse frequency of 5 Hz was
used for the growth. The oxygen pressure was controlled at 25 Pa during the deposition
process. The substrates were cleaned in pure ethanol with an ultrasonic bath to remove
physisorbed organic molecules from the Si surfaces. Then the substrates were rinsed several
times with de-ionized water. Finally the wafers were dried in a pure nitrogen stream before
the deposition of the LSCO ﬁlms. The ceramic LSCO target with a La:Sr stoichiometric ratio
of 0.5:0.5 was sintered by solid state reaction. The substrate temperature was kept at 700
◦
C.
In order to obtain the nominal thickness of about 1 μm, the LSCO layers have been deposited
during the several periods.
On the other hand, the sol-gel technique is applied to fabricate the LNO with different
thickness on platinized silicon (Pt/Ti/SiO
2
/Si) substrates. Lanthanum nitrate [La(NO
3
)
3
] and
nickel acetate [Ni(CH
3
COO)
2
•4H
2
O] were used as the start materials, and acetic acid and
water were used as the solvents. Nickel acetate was dissolved in acetic acid and equimolar
amounts of lanthanum nitrate dissolve in distilled water held at RT, respectively. Then the
two solutions were mixed together with constant stirring. The concentration of the precursor
solution was adjusted to 0.3 M by adding or distilling some acetic and water. The LNO
ﬁlms were deposited spin coating of the 0.3 M solution at the speed of 4000 rpm for 30 s.
Each layer of the ﬁlms was dried at 160
◦
C for 5 min, then pyrolyzed at 400
◦
C for 6 min to
remove residual organic compounds, following annealed at 650
◦
C for 3 min in air by a rapid
thermal annealing (RTA) process. The aforementioned coating, pyrolyzing and annealing
were repeated different times in order to obtain the LNO ﬁlms with different thickness.
2.3 The crystalline and optical characterizations
The crystallinity of the BLT, LNO, and LSCO ﬁlms at RT was examined by XRD using a Ni
ﬁltered Cu Kα radiation source (D/MAX-2550V, Rigaku Co.). In the XRD measurement a
vertical goniometer (Model RINT2000) was used, and continuous scanning mode (θ-2θ) was
selected with a scanning rate of 10
◦
/min and interval of 0.02
◦
. The temperature dependent
ultraviolet transmittance spectra were measured by a double beam ultraviolet-infrared
spectrophotometer (PerkinElmer UV/VIS Lambda 2S) at the photon energy range of 1.1-6.5 eV
66 Ferroelectrics
Optical Properties and Electronic Band Structures
of Perovskite-Type Ferroelectric and Conductive Metallic Oxide Films 5
Fig. 1. The XRD patterns of Bi
3.25
La
0.75
Ti
3
O
12
, LNO and La
0.5
Sr
0.5
CoO
3
ﬁlms, respectively.
(190-1100 nm). The BLT ﬁlm was mounted into an optical cryostat (Optistat CF-VfromOxford
Instruments) and the temperature was continuously varied from 80 to 480 K. Near-normal
incident optical reﬂectance spectra (∼ 8
◦
) were recorded at room temperature (RT) with a
double beam ultraviolet-infrared spectrophotometer (PerkinElmer Lambda 950) at the photon
energy from 0.47 to 6.5 eV (190-2650 nm) with a spectral resolution of 2 nm. Aluminum
(Al) mirror, whose absolute reﬂectance was directly measured, was taken as reference for the
spectra in the photon energy region. The ellipsometric measurements were carried out at RT
by a variable-angle infrared spectroscopic ellipsoetry (IRSE) synchronously rotating polarizer
and analyzer. The system operations, including data acquisition and reduction, preampliﬁer
gain control, incident angle, wavelength setting and scanning were fully and automatically
controlled by a computer. In this study, the incident angles were 70
◦
, 75
◦
and 80
◦
for the LNO
ﬁlms. Note that no mathematical smoothing has been performed for the experimental data.
3. The crystalline structures
Figure 1 (a) shows the XRD spectra of BLT, LNO, and LSCO nanocrystalline ﬁlm. For the BLT
ﬁlm, there are the strong diffraction peaks (004), (006), (008), (117) and (220), which conﬁrm
that the present BLT nanocrystalline ﬁlm has the tetragonal phase. Note that the broadening
feature near 22
◦
can be ascribed to the quartz substrate. On the other hand, the XRD patterns
indicate that the LNO and LSCO ﬁlms are crystallized with the single perovskite phase. It
should be emphasized that the LNO ﬁlm presents a highly (100)-preferential orientation.
Besides the strongest (110) peak, some weaker peaks (100), (111), (200), and (211) appear,
indicating that the LSCO ﬁlm is polycrystalline. Generally, the grain size can be estimated by
the well-known Scherrer’s equation r = Kλ/βcosθ, where r is the average grain size, β the full
width at half maximum of the diffraction line, λ the x-ray wavelength, θ the Bragg angle, K
the Scherrer’s constant of the order of unity for usual crystals. For the BLT ﬁlm on the quartz
substrate, the average grain size from the (006) diffraction peak is estimated to about 16 nm.
However, the grain size from the (200) and (110) peaks was evaluated to 78 and 27 nm for the
LNO and LSCO ﬁlms on Si substrates, respectively. Note that the grain size of the BLT and
LSCO ﬁlms is much less that that of the LNO ﬁlm. The striking increment for the LNO ﬁlm
67
Optical Properties and Electronic Band Structures of
Perovskite-Type Ferroelectric and Conductive Metallic Oxide Films
6 Ferroelectrics
could be due to the better crystallization (i.e., highly preferential orientation). It should be
emphasized that the LNO ﬁlms on the Pt/Ti/SiO
2
/Si substrates are of the similar crystalline
structure to that from the silicon substrate. Nevertheless, the grain size of the LNO ﬁlms on
the Pt/Ti/SiO
2
/Si substrates is estimated to 18.4, 17.5 nm and 27.8 nm for the 100-nm, 131-nm
and 177-nm thick ﬁlms, respectively. It indicates that the average grain size is similar for the
LNO ﬁlms with the thickness of about 200 nm on different substrates.
4. Transmittance, reﬂectance and SE theory
4.1 Transmittance and reﬂectance
Generally, transmittance and reﬂectance spectra can be reproduced by a three-phase layered
structure (air/ﬁlm/substrate) for the ﬁlm materials with a ﬁnite thickness. (40; 41; 42) For the
BLT ﬁlm, the three-phase layered structure conﬁguration is applied due to the thickness of
about 150 nm. Nevertheless, it is noted that the nominal growth thickness is about 230 nm
and 1 μm for the LNO and LSCO ﬁlms on Si substrates, respectively. Therefore, considering
the light penetration depth in the ﬁlms due to the optical conductivity, the three-phase layered
model and the semi-inﬁnite medium approach are applied to calculate the reﬂectance spectra
of the LNO and LSCO ﬁlms, respectively. (27; 51) The optical component of each layer is
expressed by a 2×2 matrix. Suppose the dielectric function of the ﬁlm is ˜ ε, vacuum is unity,
and the substrate is ˜ ε
s
, respectively. The resultant matrix M
r
is described by the following
product form
M
r
= M
v f
M
f
M
f s
. (1)
Here, the interface matrix between vacuum and ﬁlm has the form
M
v f
=
1
2
√
˜ ε
_
(
√
˜ ε +1) (
√
˜ ε −1)
(
√
˜ ε −1) (
√
˜ ε +1)
_
. (2)
and the propagation matrix for the ﬁlm with thickness is described by the equation
M
f
=
_
exp(i2π
√
˜ εd/λ) 0
0 exp(−i2π
√
˜ εd/λ)
_
. (3)
where λ is the incident wavelength, and correspondingly the interface matrix between ﬁlm
and substrate is
M
f s
=
1
2
√
˜ ε
s
_
(
√
˜ ε
s
+
√
˜ ε) (
√
˜ ε
s
−
√
˜ ε)
(
√
˜ ε
s
−
√
˜ ε) (
√
˜ ε
s
+
√
˜ ε)
_
. (4)
thus, the transmittance T and reﬂectance R can be readily obtained from
T = Real(
√
˜ ε)
¸
¸
¸
¸
1
M
r1,1
¸
¸
¸
¸
2
, R =
¸
¸
¸
¸
M
r1,0
M
r1,1
¸
¸
¸
¸
2
. (5)
The multi-reﬂections fromsubstrate are not consideredin Eq (5). It should be emphasized that
the absorption from the substrate must be taken into account to calculate the transmittance of
the ﬁlm-substrate system. (44)
The physical expression of the real and imaginary parts of the dielectric functions for
semiconductor and insulator materials has been reported by Adachi. (52) The Adachi’s model
dielectric function is based upon the one electron interband transition approach, and relies
upon the parabolic band approximation assuming energy independent momentum matrix
elements. In our present spectral range, the dielectric functions of the nanocrystalline ﬁlm
68 Ferroelectrics
Optical Properties and Electronic Band Structures
of Perovskite-Type Ferroelectric and Conductive Metallic Oxide Films 7
are primarily ascribed to the fundamental optical transition. Moreover, for wide band gap FE
materials, the dielectric response can be described by the contribution from typical critical
point (CP). Therefore, the Adachi’s model is employed to express the unknown dielectric
functions of the BLT nanocrystalline ﬁlm, and written as
˜ ε(E) = ε
∞
+
A
0
_
2 −
√
1 +χ
0
(E) −
√
1 −χ
0
(E)
_
√
E
3
0
χ
0
(E)
2
. (6)
Here, χ
0
= (E +iΓ)/E
0
, A
0
and Γ are the strength and broadening values of the E
0
transition,
respectively. (52) It should be emphasized that the dielectric functions of many semiconductor
and dielectric materials have been successfully determined by ﬁtting the Adachi’s model to
the measured data. (53; 54; 55; 56; 57; 58) On the other hand, the dielectric function of the
metallic oxide ﬁlms can be expressed using a Drude-Lorentz oscillator dispersion relation
owing to the conductivity
ε(E) = ε
∞
−
A
D
E
2
+ iEB
D
+
4
∑
j=1
A
j
E
2
j
−E
2
−iEB
j
. (7)
Here ε
∞
is the high-frequency dielectric constant, A
j
, E
j
, B
j
, and E is the amplitude, center
energy, broadening of the jth oscillator, and the incident photon energy, respectively. (27; 29;
59) The refractive index n and extinction coefﬁcient k can be calculated as follows
n =
1
√
2
_
_
ε
1
2
+ε
2
2
+ε
1
, k =
1
√
2
_
_
ε
1
2
+ε
2
2
−ε
1
. (8)
where ε
1
and ε
2
are the real part and imaginary part of the dielectric function, respectively.
The root-mean-square fractional error σ, deﬁned by
σ
2
=
1
N − M
N
∑
i=1
(T(R)
m
i
−T(R)
c
i
)
2
. (9)
where T(R)
c
i
and T(R)
m
i
are the calculated and measured values at the ith data point for
the transmittance or reﬂectance spectra. N is the number of wavelength values and M is
the number of free parameters. (11; 60; 61) A least squares-ﬁtting procedure employing the
modiﬁed Levenberg-Marquardt algorithm, the convergence of which is faster than that of the
SIMPLEX algorithm, was used in the transmittance or reﬂectance spectral ﬁtting.
4.2 SE technique
On other hand, SE, based on the reﬂectance conﬁguration, provides a effective tool to extract
simultaneously thickness and optical constants of a multilayer system. (48) It is a sensitive and
nondestructive optical method that measures the relative changes in the amplitude and the
phase of particular directions polarized lights upon oblique reﬂection fromthe sample surface.
The experimental quantities measured by ellipsometry are the complex ratio ˜ ρ(E) in terms of
the angles Ψ(E) and Δ(E), which are related to the structure and optical characterization of
materials and deﬁned as
˜ ρ(E) ≡
˜ r
p
(E)
˜ r
s
(E)
= tanΨ(E)e
iΔ(E)
. (10)
69
Optical Properties and Electronic Band Structures of
Perovskite-Type Ferroelectric and Conductive Metallic Oxide Films
8 Ferroelectrics
here, ˜ r
p
(E) and ˜ r
s
(E) is the complex reﬂection coefﬁcient of the light polarized parallel and
perpendicular to the incident plane, respectively. (50) It should be noted that ˜ ρ(E) is the
function of the incident angle, the photon energy E, ﬁlm thickness and optical constants ˜ n(E),
i.e., the refractive index n and extinction coefﬁcient κ from the system studied. Generally, the
pseudodielectric function
˜
< ε > is a useful representation of the ellipsometric data Ψ and Δ
by a two-phase (ambient/substrate) model (50)
˜
< ε > =<ε
1
> +i < ε
2
>= sin
2
ϕ
_
1 +
_
1 − ˜ ρ
1 + ˜ ρ
_
2
tan
2
ϕ
_
. (11)
where ϕ is the incident angle. Although ˜ ρ(E) and ˜ n(E) may be transformed, there are no
corresponding expressions for ˜ n(E), which is distinct for different materials. (62) Therefore,
the spectral dependencies of Ψ(E) and Δ(E) have to be analyzed using an appropriate ﬁtting
model. Correspondingly, the ﬁlm thickness d
f
, optical constants and other basic physical
parameters, such as optical band gap, the high frequency dielectric constant ε
∞
, etc., can
be extracted from the best ﬁt between the experimental and ﬁtted spectra. Similarly, the
three-phase layered structure model cab be applied to reproduce the SE spectra of the LNO
ﬁlms on the Pt/Ti/SiO
2
/Si substrates due to a smaller thickness (the maximum value is about
180 nm). In SE ﬁtting, the root-mean-square fractional error, which is deﬁned as
σ
2
=
1
2J −K
J
∑
i=1
⎡
⎣
_
Ψ
m
i
−Ψ
c
i
σ
m
Ψ,i
_
2
+
_
Δ
m
i
−Δ
c
i
σ
m
Δ,i
_
2
⎤
⎦
. (12)
has been used to judge the quality of the ﬁt between the measured and model data. (11)
Where, J is the number of data points and K is the number of unknown model parameters, has
been used to judge the quality of the ﬁt between the measured and model data. Note that Eq.
12 has 2J in the pre-factor because there are two measured values included in the calculation
for each and pair. The standard deviations were calculated from the known error bars on
the calibration parameters and the ﬂuctuations of the measured data over averaged cycles of
the rotating polarizer and analyzer. Note that the same Levenberg-Marquardt algorithm as
the above T or R data was applied to reproduce SE spectra. Therefore, the infrared optical
constants of the LNO ﬁlms can be uniquely extracted.
5. Optical properties of the BLT ﬁlms
Typical transmittance spectra of the BLT ﬁlms at different temperatures are shown in Fig. 2
(a). The spectra can be roughly separated into three speciﬁc regions: a transparent oscillating
one (labeled with “I”), a low transmittance one (“II”), and a strong absorption one (“III”) at
higher photon energies. The Fabry-P´ erot interference behavior observed in the transparent
region, which is due to the multi-reﬂectance between the ﬁlm and substrate, is similar to
those on silicon substrates. (10; 63) The transmittance differences with the temperature
are ascribed to the thermal expansion and variations of optical constants in lower photon
energies. Transmittance spectra ranging from 80 to 480 K were measured in order to analyze
the shift of the absorption edge during the phase transition. As shown in Fig. 3 (a),
the spectral transmittance value sharply decreases with the photon energy and down to
zero in the ultraviolet region beyond 4.5 eV. This is due to the strong absorption from the
fundamental band gap and high-energy CP transitions, which can not be detected by the
present transmittance spectra.
70 Ferroelectrics
Optical Properties and Electronic Band Structures
of Perovskite-Type Ferroelectric and Conductive Metallic Oxide Films 9
Fig. 2. Transmittance spectra of the BLT ﬁlm at the temperature region from 77 to 500 K: (a) in
the ultraviolet-infrared photon energy of 1.1-6.5 eV, and (b) near the OBG region of 3.6-4.5 eV.
The arrows indicate the corresponding temperature values. (Figure reproduced with
permission from (63). Copyright 2007, American Institute of Physics.)
Fig. 3. (a) Experimental (dotted line) and ﬁtting (solid line) transmittance spectra of the BLT
ﬁlm at 300 K. (b) The optical transition energy E
0
of the Adachi’s model for the BLT ﬁlm with
different temperatures. It indicates that the optical transition energy E
0
decreases with
increasing the temperature. Nevertheless, the anomalous behavior can be observed around
160 and 300 K. (c) The strength parameter A
0
of the E
0
transition with different temperatures.
71
Optical Properties and Electronic Band Structures of
Perovskite-Type Ferroelectric and Conductive Metallic Oxide Films
10 Ferroelectrics
Temperature (K) A
0
(eV
3/2
) E
0
(eV) Γ (eV) S E
c
(eV) E
d
(eV) n(0)
80 113.5 3.85 0.08 3.18 4.71 7.48 2.18
90 116.1 3.85 0.06 3.25 4.68 7.51 2.20
100 116.2 3.83 0.05 3.28 4.66 7.47 2.21
110 116.6 3.84 0.05 3.29 4.65 7.46 2.21
120 116.5 3.83 0.05 3.30 4.64 7.43 2.21
130 116.2 3.83 0.05 3.30 4.62 7.31 2.20
140 114.2 3.82 0.04 3.28 4.62 7.21 2.20
150 108.4 3.80 0.05 3.20 4.58 6.76 2.17
160 96.7 3.73 0.05 3.10 4.43 5.66 2.09
170 120.6 3.84 0.07 3.34 4.68 7.87 2.24
180 121.5 3.84 0.07 3.35 4.68 7.91 2.25
190 122.8 3.85 0.08 3.37 4.69 8.03 2.25
200 123.3 3.85 0.08 3.38 4.70 8.09 2.26
210 123.3 3.84 0.07 3.40 4.68 8.02 2.26
220 122.6 3.83 0.07 3.40 4.67 7.95 2.26
230 121.8 3.83 0.07 3.39 4.66 7.89 2.25
240 120.8 3.82 0.08 3.38 4.65 7.81 2.25
250 119.3 3.82 0.08 3.36 4.64 7.68 2.24
260 118.2 3.81 0.07 3.36 4.61 7.53 2.23
270 116.6 3.80 0.07 3.35 4.60 7.39 2.23
280 115.0 3.79 0.07 3.34 4.58 7.23 2.22
290 112.7 3.78 0.07 3.32 4.55 7.00 2.20
300 110.0 3.75 0.05 3.33 4.49 6.62 2.19
310 109.3 3.73 0.04 3.37 4.44 6.41 2.19
320 108.3 3.72 0.03 3.39 4.41 6.21 2.19
330 107.6 3.71 0.03 3.40 4.38 6.09 2.19
340 107.2 3.71 0.03 3.41 4.36 5.99 2.19
350 106.3 3.70 0.03 3.41 4.35 5.88 2.18
360 106.3 3.69 0.02 3.44 4.33 5.80 2.19
370 105.9 3.69 0.02 3.45 4.31 5.71 2.19
380 105.6 3.68 0.02 3.46 4.29 5.63 2.18
390 105.3 3.68 0.02 3.38 4.28 5.53 2.18
400 104.6 3.67 0.02 3.48 4.27 5.45 2.18
410 104.7 3.66 0.02 3.50 4.25 5.37 2.18
420 104.5 3.66 0.02 3.52 4.23 5.30 2.18
430 104.5 3.66 0.02 3.52 4.23 5.30 2.18
440 104.5 3.66 0.02 3.52 4.23 5.31 2.19
450 104.6 3.67 0.02 3.50 4.25 5.41 2.18
460 105.3 3.66 0.04 3.50 4.26 5.51 2.19
470 105.5 3.66 0.04 3.51 4.25 5.51 2.19
480 105.4 3.66 0.04 3.51 4.25 5.51 2.19
Table 1. The Adachi’s model parameters of the BLT ﬁlm at the temperature range of 80-480 K
are determined from the simulation of the transmittance spectra. Note that the thickness is
estimated to 145 nm and the ε
∞
is ﬁxed to 1 for the ﬁlm measured at different temperature.
In addition, S, E
c
, E
d
, and n(0) is the contribution from high-energy CP transitions, the
oscillator energy, the dispersion energy of the Sellmeier relation, and long wavelength
refractive index. respectively.
72 Ferroelectrics
Optical Properties and Electronic Band Structures
of Perovskite-Type Ferroelectric and Conductive Metallic Oxide Films 11
The ﬁtted parameter values in Eq. 6 are summarized in Table 1 and Fig. 3 (b) and (c). A good
agreement is obtained between the measured and calculated data in the experimental range,
especially for the fundamental band gap region. For all temperatures, the ﬁtting standard
deviations are less than 2 ×10
−3
. As can be seen in Fig. 3 (b), the optical transition energy E
0
of
the BLT ﬁlm increases with decreasing temperature except for the temperatures of 160 and 300
K. Fig. 3 (b) can be roughly separated into three speciﬁc regions: the monoclinic phase (labeled
with ”A”), the orthorhombi phase (labeled with ”B”) and the tetragonal phase (labeled with
”C”). An obvious dip at 160 K for the fundamental band gap can be observed due to the
phase/structural transition. (20) The origin of the structural anomaly is due to strain energy
and lattice strain change with the temperature. The variation of E
0
with temperature can be
mainly ascribed to thermal expansion and electron-phonon (e-p) interaction. The BLT ﬁlm
emits or absorbs the phonon with increasing temperature. It will result in the band gap
perturbation and shift. The valence-band top mainly consists of the O
2p
orbital, which is
strongly hybridized with the Ti
3d
orbital below the Fermi level. (13) The strong hybridization
between the O
2p
and Ti
3d
orbitals changes with the distortion of the crystal structure during
the phase transition. Therefore, the E
0
variation clearly indicates that the absorption edge is
strongly related to the phase transition with decreasing temperature.
It is generally believed that the symmetry of BiT at RT is orthorhombic and changes to
tetragonal at 675
◦
C. (64) As we know, physical properties of FE nanocrystals are strongly
dependent on the grain size. (65) Recently, a size-driven phase transition was found at a
critical size r
c
of 44 nm for BiT. The high-temperature tetragonal phase stabilizes at RT when
the grain size is smaller than the r
c
. (17) According to the XRD analysis, the BLT ﬁlm has the
tetragonal crystal structure at RT. Various anomalies of BiT at low temperature are believed
to be a possible indication of the structural transitions. For instance, the dielectric constant
decreases with decreasing temperature except for a broad hump around about 150 K, the
spontaneous polarization (P
s
) changes little but for a gradual decrease in the 100-250 K range
with some thermal hysteresis and the E
c
gradually decreases to a minimum at 100 K except
for the broad hump about 200 K. (20) The similar phenomena from the optical properties
can be observed in the present BLT nanocrystalline ﬁlm. Note that the parameter A
0
of the
Adachi’s model is anomalous at 160 and 300 K. Moreover, the E
0
continuously decreases
with increasing temperature except for the values at the temperatures of 160 and 300 K. The
dielectric function anomaly indicates that the BLT nanocrystalline ﬁlm undergoes a tetragonal
to orthorhombic phase transition in the temperature range of 200-250 K. (21) Thermodynamic
analysis indicate that the energy separation of the orthorhombic and monoclinic states
decreases with decreasing the temperature. (66) When the temperature further decreases,
the BLT nanocrystalline ﬁlm with orthorhombic structure undergoes monoclinic distortion
around 160 K. (21) From the dielectric function model, one can safely conclude that the low
temperature phase transition of the BLT ﬁlm can be detected by the spectral transmittance.
The calculated dielectric functions are exhibited in Fig. 4. The real part ε
1
increases and
reaches a maximum, beyond which it gradually falls with further increasing of the photon
energy. The peak position of ε
1
corresponding approximately with the optical transition
energy E
0
of the BLT ﬁlm shifts to high energies with decreasing the temperature. The peaks
may be assigned to the transitions between the CP or lines with high symmetry in the Brillouin
zone, termed as Van Hove singularities. In the present case, the value of the photon energy
corresponding to the peaks of ε
1
is about 3.7 eV, which agrees with the value of the FE band
gap (3-4 eV). (67). Therefore, the CP may be associated with the interband transition between
the valence and conduction bands of BLT nanocrystalline ﬁlm. The sites of the dielectric
73
Optical Properties and Electronic Band Structures of
Perovskite-Type Ferroelectric and Conductive Metallic Oxide Films
12 Ferroelectrics
Fig. 4. Temperature dependence of dielectric function (a) real part and (b) imaginary part for
the BLT nanocrystalline ﬁlm in the photon energy range of 1.1-6.5 eV. The anomalies of
dielectric function are observed at 160 and 300 K, respectively.
function or the refractive index peaks generally correspond to the band gap energies of the
dielectrics and semiconductors. (68; 69) This can be understood from the K-K relation (70; 71)
n(v) = 1 +
c
π
_
dα(v

)
dv

log(
v

+ v
v

−v
)dv

. (13)
where c is the light velocity in vacuum, v and v

are light frequencies, α(v

) is the absorption
coefﬁcient. In the frequency region near the absorption edge the value of dα(v

)/dv

is very
large; however, when the photon energy reaches the gap energy, the absorption curve changes
its slope and becomes smoother, so the value of dα(v

)/dv

decreases at the absorption edge.
The imaginary part ε
2
is nearly zero in the interference region and increases rapidly with E,
reaches a maximum, and falls slightly at higher energies. The ε
2
near the fundamental band
gap energy is not zero due to defects and disorder in the nanocrystalline ﬁlm. Moreover,
the real part of ε decreases with the temperature and varies from 9.04 at 480 K to 8.22 at
80 K at the photon energy of 3.7 eV. The reduction is due to decreasing electron-phonon
interactions at degraded temperatures, making direct transitions less probable. From Fig.
4, an anomaly of the dielectric function is observed at 160 and 300 K, which can be ascribed
to the phase/strucutural transitions. Fig. 5 exhibits the temperature-dependent refractive
index n at various photon energies. The anomalous variations occur at the temperature rang
of 130-160 K and 290-330 K, indicating the subtle phase transitions in the corresponding
temperature regions, as compared with lower-temperature Raman results. (20; 21) As
previously discussed, the optical constants are strongly related to the crystalline structure,
which can affect the valence and conduction band formation. Obviously, the structural
variation of the BLT ﬁlm can contribute to the optical response.
74 Ferroelectrics
Optical Properties and Electronic Band Structures
of Perovskite-Type Ferroelectric and Conductive Metallic Oxide Films 13
Fig. 5. Variation of the refractive index for the BLT nanocrystalline ﬁlm with the temperature
at the photon energies of 3.9, 5, and 6 eV, respectively.
In order to give an insight on the electronic band structure of the BLT ﬁlm, we have ﬁtted the
refractive index n belowthe optical transition energy with a dispersionformula corresponding
to an empirical Sellmeier equation
n
2
= S +
E
c
E
d
E
2
c
−E
2
. (14)
Here, S is the contribution from high-energy CP transitions, E
c
the oscillator energy, and E
d
the dispersion energy. The ﬁtting quality from the BLT ﬁlm at 80 K has been illustrated in
Fig. 6 (a). The empirical Sellmeier equation gives a relatively good description to the optical
Fig. 6. (a) An empirical Sellmeier equation in the transparent region for BLT nanocrystalline
ﬁlm at 80 K. (b) The long wavelength refractive index n(0) with different temperatures. The
anomalous n(0) values occur at 160 and 300 K, respectively.
75
Optical Properties and Electronic Band Structures of
Perovskite-Type Ferroelectric and Conductive Metallic Oxide Films
14 Ferroelectrics
Fig. 7. Experimental (dotted lines) and best-ﬁt (solid lines) near-normal incident reﬂectance
spectra of LNO and La
0.5
Sr
0.5
CoO
3
ﬁlms. The arrow is applied to approximately distinguish
two different electronic transition regions. (Figure reproduced with permission from (25).
Copyright 2009, American Institute of Physics.)
dispersion in the transparent range. The parameters of Sellmeier equation are summarized in
Table 1. The S value generally increases with the temperature except for the phase transitions,
indicating that the effects from high-frequency electronic transitions becomes stronger in the
BLT ﬁlm. It can be found that the maximum optical transition occurs near the energy range
of 4.2-4.7 eV from the ﬁtted oscillator energy, which agrees well with ε
2
observed (see Fig.
4). It indicates that the optical dispersion in the transparent region is mainly ascribed to the
higher CP virtual transitions and not by the band gap energy. Note that the parameter S
presents an opposite variation trend with the temperature, as compared with the oscillator
energy E
c
and the dispersionenergy E
d
apart fromthe temperature ranges around 160 and 300
K. Again, the anomaly can be ascribed to the phase transitions as previously discussed. The
long wavelength refractive index n(0), which can be calculated from
√
(E
d
/E
c
) + S, is shown
in Fig. 6 (b). The n(0) at 300 K is estimated to be about 2.19 at zero point, which indicates that
the dielectric function is about 4.80. The n(0) is related to the total effective number of valence
electrons per atom in materials. For theoretically calculating n(0), the f -sum-rule integral can
be written as
n
2
(0) −1 =
4
π
_
∞
0
n(ω

As such, these films
have potential to serve as a medium for scanning probe microscopy (SPM)-based ultrahigh
density (100 Gbit/cm
2
class) data storage [2]. It has been proposed that employing
ferroelectric films as recording media inherently has several advantages: 1) the recorded
data are non-volatile, 2) the recording density can be ultra high because of narrow domain
wall thickness, 3) the ferroelectric domains can have fast switching speeds, and 4)
information bits can be written and read electrically.
Among the various perovskite oxide materials, PZT films appear to be suitable as a storage
medium, since their remanent polarizations are high. The highly tetragonal PZT films
exhibit high remanent polarization showing a square-shaped hysteresis curve, compared
with films having morphotropic and rhombohedral compositions. Therefore, Pb(Zr
0.2
Ti
0.8
)O
3

substrates. In order to achieve epitaxial growth of SrRuO
3
on Si, yttria-stabilized zirconia (YSZ)
[7-8] and MgO [9] have been employed as buffer layer materials. Another promising candidate
for the buffer layer is SrO which has a NaCl-type cubic structure with a lattice parameter of a =
5.140 Å [10-11].

The

SrO(110) dielectric layer also exhibits good compatibility with Si(001)
showing a low lattice mismatch of about 0.4 % [12].

In this study, highly tetragonal Pb(Zr
0.2
Ti
0.8
)O
3
films were grown on epitaxial SrRuO
3
thin
film electrodes using a SrO buffer layer on Si(001) substrates by pulsed laser deposition. The
effect of the SrO buffer layer on the surface morphologies and the electrical properties of the
Ferroelectrics

90
SrRuO
3
thin film electrodes was investigated as a function of SrO buffer layer thickness.
Ferroelectric properties in c-axis oriented Pb(Zr
0.2
Ti
0.8
)O
3
thin films deposited on an epitaxial
SrRuO
3
electrode were also investigated.
2. Experimental procedure
The SrO target for pulsed laser deposition is difficult to make due to the low sinterability of
SrO materials. A SrO
2
target was used to deposit SrO on Si (001) substrates in a vacuum
ambient. Before deposition of SrO layers on Si (001) substrates, Si wafers were etched using
HF solution to remove the native oxide layers. SrO, SrRuO
3
and PZT films were deposited
on etched-silicon substrates using a KrF excimer laser (λ = 248 nm) with a maximum
repetition rate of 10 Hz. Laser pulse energy density used for SrO, SrRuO
3
and PZT films
deposited using ceramic targets was approximately 1.5 J/cm
2
. 30 mol % excess PbO in the
PZT targets was added to compensate for the PbO loss during both the sintering and
deposition processes. The distance between the target and substrate was varied depending
on the deposited materials. The typical SrO, SrRuO
3
, and PZT deposition conditions are
summarized in Table 1. The SrO, SrRuO
3
, and PZT were in-situ deposited at each
temperature in order to ensure chemical stability of the SrO films with Si. The PZT films
were cooled down to room temperature at an oxygen pressure of 300 Torr to preserve the
oxygen content in the films during the cooling procedure.
Deposition parameters SrO SrRuO
3
Pb(Zr
0.2
Ti
0.8
)O
3

91
3. Results and discussion
Figure 1(A) shows XRD patterns of 100 nm thick-SrRuO
3
thin films deposited on SrO buffer
layers with various thicknesses. The XRD patterns were plotted using a log-scale to check the
existence of the minor portion of SrO
2
phase within the SrRuO
3
films. The SrRuO
3
films were
deposited at about 650
o
C in 1 × 10
-2
Torr. As shown in Fig. 1(A), SrRuO
3
films deposited on 6
nm-thick-SrO buffered Si (001) substrates exhibit a c-axis preferred orientation, indicating the
(001) and (002) planes alone. In the case of buffer layers above 12 nm thickness, SrO
2
phase
was observed in the SrRuO
3
films. From the XRD results, the SrO buffer layer was found to
play an important role for the preferred growth of SrRuO
3
films on Si substrates at below
approximately 6 nm-thickness. In order to investigate the epitaxial relationship between
SrRuO
3
and SrO(6 nm)/Si(001), a Φ-scan in the SrRuO
3
/SrO/Si structure was performed and
the results are shown in Fig. 1 (B). Peaks of SrRuO
3
{111} can be observed at every 90
o
,
indicating that the SrRuO
3
films are epitaxially grown on a SrO/Si (001).

92
Figure 2 shows the variation in resistivity and rms roughness of 100nm thick-SrRuO
3
thin films
as a function of SrO thickness. The SrRuO
3
films deposited on ultra-thin SrO films of about
3nm show the highest rms roughness and resistivity values because the SrO films do not play
a role as a buffer layer. On the other hand, above 6nm thickness, SrRuO
3
films exhibit a low
rms roughness of about 3-5 Å and a resistivity of 1700 – 1900 μΩ-cm. The resistivity values of
the SrRuO
3
films deposited on 6nm-thick SrO buffer layers are approximately 1700 μΩ-cm,
higher than that of SrRuO
3
films (~ 400 μΩ-cm) deposited on SrTiO
3
single crystals[13] and
(100) LaAlO
3
single crystals[14]. The high resistivity of the SrRuO
3
films on Si substrates
originates from the existence of silicon oxide formed from the diffusion of silicon, because the
thin SrO layer does not prevent the diffusion of silicon during the deposition of SrRuO
3
at high
temperature. The full-width-half-maximum (FWHM) values of the SrRuO
3
films deposited on
SrO/Si and SrTiO
3
single crystal substrates are approximately 7.32
o
and 0.15
o
, measured by ω-
scan, respectively. These results suggest that the SrRuO
3
films grown on Si substrates are
inferior in terms of film qualities such as crystallinity and defects relative to those grown on
SrTiO
3
single crystals. The inset in Fig. 2 shows three-dimensional AFM images of SrRuO
3

films exhibits a constant value of about 1700 μΩ-cm irrespective of the film thickness above
50nm. The rms roughness of the SrRuO
3
films exhibits a similar tendency with the variation
of resistivity as a function of SrRuO
3
thickness. The film roughness in conducting materials
is inversely proportional to the mobility of the charge carriers. The resistivity in the
conducting films is also inversely proportional to the mobility of the charge carriers if the
concentration of the charge carriers is constant.
0 5 10 15 20 25 30
0.0
0.5
1.0
1.5
Rms roughness

Fig. 3. (a) XRD patterns, (b) rms roughness and resistivity of the SrRuO
3
films deposited on
6nm-thick SrO buffer layers as a function of SrRuO
3
thickness
Figure 4(a) and 4(b) show XRD patterns and variation of rms roughness and resistivity,
respectively, for 190nm-thick SrRuO
3
films as a function of SrRuO
3
deposition temperature.
As shown in Fig. 4(a), SrRuO
3
films deposited at 550 and 600
o
C show SrRuO
3
(110) peaks in
addition to the SrRuO
3
{001} peaks. This indicates that the films deposited at lower
temperatures exhibit a polycrystalline nature rather than an epitaxial relationship. The
SrRuO
3
(110) peak disappears in the films deposited above 650
o
C and the films are grown
with an epitaxial relationship with Si (001) substrates. As shown in Fig. 4(b), the rms
roughness of the films continuously increases with increasing deposition temperature, and a
rms roughness of 7.4 Å is noted in the films deposited at 650
o
C. The rms roughness of the
SrRuO
3
films deposited on SrO/Si substrates is higher than that of the films deposited on
SrTiO
3
single crystals [13]. In the SrRuO
3
/SrO/Si structure, even though the films deposited
above 650
o
C were epitaxially grown, the high rms roughness of the SrRuO
3
films was
(a)
10 20 30 40 50 60
S
r
R
u
O
3
(
0
0
2
)

94
attributed to the unstable interface structure of SrO/Si, compared with the SrTiO
3
single
crystal substrate. The resistivity of the SrRuO
3
films abruptly decreases as the deposition
temperature increases up to 650
o
C and maintains a constant value of about 1700 μΩ-cm at
deposition temperatures above 650
o
C.The SrRuO
3
films grown with an epitaxial relationship
exhibit lower resistivity than the polycrystalline films.

95
was fitted by repeated adjustments with the standard composition of SrRuO
3
. The results
suggest that the epitaxial SrRuO
3
films deposited by pulsed laser deposition show the same
composition as SrRuO
3
targets.

96
relationship with SrRuO
3
{001} at deposition temperatures of 575 and 600
o
C. The Pt (111)
peak originates from the top electrode in the Pt/PZT/SrRuO
3
/SrO/Si capacitor structures.
However, the peak intensities of PZT{001} decrease with increasing deposition temperature.
The PZT films react with the SrRuO
3
bottom electrode at high deposition temperature,
resulting in Pb diffusion into the SrRuO
3
/SrTiO
3
[15]. Even though Pb is diffused into the
SrRuO
3
films, PZT films deposited on SrRuO
3
/SrTiO
3
exhibit a good epitaxial relationship
maintaining the predominating crystallinity. In order to investigate the distributions of each
element in the PZT films deposited on SrRuO
3
/SrO/Si, the elemental distribution in each
layer was analyzed by secondary ion mass spectroscopy (SIMS), as shown in Fig. 7 (a). The
Pb from the PZT films deposited at 600
o
C was clearly observed within the SrRuO
3
layer,
indicating similar diffusion behavior of Pb into the SrRuO
3
/SrTiO
3

[15]. In addition, silicon
was also observed at the PZT layer as well as at the SrRuO
3
layer. The silicon existing in the
PZT and SrRuO
3
films will present as silicon oxide, because silicon oxide phase is
thermodynamically stable compared with Si element. The silicon oxide will exert a harmful
influence upon the crystallinity and the morphologies of the PZT films. The existence of
silicon in the PZT layer and Pb in the SrRuO
3
layer was also verified by the AES depth-
profile as shown in Fig. 7(b). A phi-scan was performed to identify whether the PZT films
are epitaxially grown on the SrRuO
3
films. From the results (not shown here), PZT films do
not exhibit epitaxial growth on the SrRuO
3
bottom electrode. The PZT films were only
grown with (00l) preferred orientation on SrRuO
3
electrodes. From the ω-scan of the PZT
films deposited at 575
o
C, the FWHM value of the PZT (002) is approximately 7.08
o
. Thus, the
crystalline quality of the PZT films deposited on SrRuO
3
/SrO/Si was distinctly influenced
by the silicon oxide within the PZT layers.

97
relative to reported values may be due to the poor crystallization of the PZT films resulting
from inclusion of silicon oxide phase. As shown in Fig. 8(b), leakage current densities of the
PZT films deposited at 575
o
C are approximately 2 × 10
-7
A/cm
2
at 1 V. The breakdown
strength of the films was approximately 150kV/cm. The lower breakdown strength of the
films may be due to the rough surface morphologies, as shown in the inset of Fig. 6.

2
Jozef Stefan Institute, 1000 Ljubljana
1
USA
2
Slovenia
1. Introduction
The electrocaloric effect (ECE) is the change in temperature and/or entropy of a dielectric
material due to the electric field induced change of dipolar states. Electrocaloric effect in
dielectrics is directly related to the polarization changes under electric field.
[1-3,6]
Hence a
large polarization change is highly desirable in order to achieve a large ECE which renders
the ferroelectric materials the primary candidates for developing materials with large ECE.
Figure 1 illustrates schematically the ECE in a dipolar material. Application of an electric
field to the material causes partial alignment of dipoles and consequently a reduction of
entropy of the dipolar system. In an isothermal condition, the dipolar material rejects heat
Q=TΔS to the surrounding, where T is the temperature and ΔS is the isothermal entropy
change. Or in an adiabatic process, to keep the total entropy of the material constant, the
temperature of the dielectric is increased by ΔT, the adiabatic temperature change which is
related to the Q = CΔT where C is specific heat capacity of the dielectric. In a reverse
process, as the applied electric field is reduced to zero and the dipoles return to the less
ordered state (or disordered state), an increase in the entropy of dipolar system occurs and
under an isothermal condition, the dielectric will absorb heat Q from the surrounding.

Fig. 1. Schematic drawing of the ECE process in a dipolar material. When E=0, the dipoles
orient randomly. When E>0, especially larger than the coercive electric field, the dipoles
orient along the electric field direction.
Ferroelectrics

100
The ECE may provide an effective means of realizing solid-state cooling devices for a broad
range of applications such as on-chip cooling and temperature regulation for sensors or
other electronic devices. Refrigerations based on ECE have the potential of reaching high
efficiency relative to vapor-compression cycle systems, and no green house emission.
Solid-state electric-cooling devices based on the thermoelectric effect (Peltier effect) have
been used for many decades (Spanner, 1951; Nolas, Sharp, and Goldsmid, 2001). However,
these cooling devices require a large DC current which results in large amount of waste heat
through Joule heating. For example, using the typical coefficient of performance (COP) for
these devices, e.g. 0.4 to 0.7, 2.4 to 3.5 watts of heat will be generated at the hot end of the
system when pumping 1 watt heat from the cold end. Hence, the thermoelectric effect based
cooling devices will not meet the requirement of high energy efficiency.
A counterpart of ECE is the MCE, which has been extensively studied for many years due to
the findings of giant magnetocaloric effect in several magnetic materials near room
temperature (Gschneidner Jr., Pecharsky and Tsokol, 2005; Pecharsky, Holm, Gschneidner
Jr. and Rink, 2003). Both ECE and MCE devices exploit the change of order parameter
brought about by an external electric or magnetic field. However, the difficulty of
generating high magnetic field for MCE devices to reach giant MCE, severely limits their
wide applications. This makes the MCE devices difficult to be used widely, especially for
miniaturized microelectronic devices, and to achieve high efficiency. In contrast, high
electric field can be easily generated and manipulated, which makes ECE based cooling
devices attractive and more practical for a broad range of applications.
This chapter will introduce the basic concept of ECE, the thermodynamic considerations on
materials with large ECE, and review previous investigations on the ECE in polar crystals,
ceramics, and thin films. A newly discovered large ECE in ferroelectric polymers will be
presented. Besides, we will also discuss different characterization techniques of ECE such as
the direct measurements and that deduced from Maxwell relations, as well as
phenomenological theory on ECEs.
2. Thermodynamic considerations on materials with large ECE
2.1 Maxwell relations
In general the Gibbs free energy G for a dielectric material could be expressed as a function
of temperature T, entropy S, stress X, strain x, electric field E and electric displacement D in
the form
,
i i i i
G U TS X x E D = − − − (1)
where U is the internal energy of the system, the stress and field terms are written using
Einstein notation. The differential form of Eq. (1) could be written as
.
i i i i
dG SdT x dX DdE = − − − (2)
Entropy S, strain x
i
and electric displacement D
i
can be easily expressed when the other two
variables are assumed to be constant,

2
1
1
.
E
E
E E
T D
T dE
c T ρ
∂ ⎛ ⎞
Δ = −
⎜ ⎟
∂
⎝ ⎠
∫
(7)
Equations (4) through (7) indicate that in order to achieve large ΔS and ΔT, the dielectric
materials should posses a large pyroelectric coefficient over a relatively broad electric field
and temperature range. For ferroelectric materials, a large pyroelectric effect exists near the
ferroelectric (F) – paraelectric (P) phase transition temperature and this large effect may be
shifted to temperatures above the transition temperature when an external electric field is
applied. It is also noted that a large ΔT may be achieved even if ΔS is small when the c
E
of a
dielectric material is small. However, as will be pointed out in the following paragraph, this
is not desirable for practical refrigeration applications where a large ΔS is required.
It is noted that in the temperature region including a first-order FE-PE transition, Eq. (6)
should be modified to take into account of the discontinuous change of the polarization ΔD
at the transition, i.e.,

0
.
E
E
dD E
S dE D
dT T
∂ ⎛ ⎞ ⎛ ⎞
Δ = − + Δ
⎜ ⎟ ⎜ ⎟
∂
⎝ ⎠ ⎝ ⎠
∫
(8)
Although a few studies on the ECE were conducted in which direct measurement of ΔT was
made (Sinyavsky, Pashkov, Gorovoy, Lugansky, and Shebanov, 1989; Xiao, Wang, Zhang,
Peng, Zhu and Yang, 1998), most experimental studies were based on the Maxwell relations
where the electric displacement D versus temperature T under different electric fields was
characterized. ΔS and ΔT were deduced from Eqs. (6) and (7) (see below for details). For
dielectric materials with low hysteresis loss and the measurement is in an ideal situation,
results obtained from the two methods should be consistent with each other. However, as
will be shown later that for the relaxor ferroelectric polymers, the ECE deduced from the
Ferroelectrics

102
Maxwell relations can be very different from that measured directly and hence the Maxwell
relations cannot be used for these materials in deducing ECE. In general, the Maxwell
relations are valid only for thermodynamically equilibrium and ergodic systems.
In an ideal refrigeration cycle the working material (refrigerant) must absorb entropy (or heat)
from the cooling load while in thermal contact with the load (isothermal entropy change ΔS).
The material is then isolated from the load while the temperature is increased due to the
application of external field (adiabatic temperature change ΔT). The material is then in thermal
contact with the heat sink and entropy that was absorbed from the cooling load is rejected to
the heat sink. The working material is then isolated from the heat sink and the temperature is
reduced back as the field is reduced. The temperature of the refrigerant will be the same as the
temperature of the cooling load when they are contacted. The whole process is repeated to
further reduce the temperature of the load. Therefore, both the isothermal entropy change ΔS
and the adiabatic temperature change ΔT are the key parameters for the ECE of a dielectric
material for refrigeration (Wood and Potter, 1985; Kar-Narayan and Mathur, 2009).
2.2 Phenomenological theory of ECE
Phenomenological theory has been widely utilized to illustrate the macroscopic phenomena
that occur in the polar materials, e.g. ferroelectric or ferromagnetic materials near their
phase transition temperatures. The general form of the Gibbs free energy associated with the
polarization can be expressed as a series expansion in terms of the electric displacement
(Line and Glass, 1977)

2
1
2
E
T TD
c
β Δ = − (10)
Based on Eqs. (9) and (10), the entropy will be reduced when the material changes to a polar
state from a non-polar state when an external action, e.g. temperature, electric field or stress,
is applied. The entropy change and temperature change are associated with the
phenomenological coefficient β and electric displacement D, viz. proportional to β and D
2
.
Both parameters will affect the ECE values of the materials. A material with large β and
large D will generate large ECE entropy change and temperature change near the
ferroelectric (F) – paraelectric (P) phase transition temperature.
2.3 ECE in several ferroelectric materials
Based on the literature reported values of β and D, the ECE values of various ferroelectric
materials could be estimated. For instance, for BaTiO
3
, β=6.7×10
5
(JmC
-2
K
-1
) and D=0.26
Electrocaloric Effect (ECE) in Ferroelectric Polymer Films

J/m
3
K (1.76 J/(kgK)) were measured directly for a sample under 25 kV/cm field at 25 °C
(Sinyavsky and Brodyansky, 1992). For Pb
0.98
Nb
0.02
(Zr
0.75
Sn
0.20
Ti
0.05
)
0.98
O
3
, ΔT =2.5 °C and
ΔS=1.73 × 10
4
J/m
3
K (2.88 J/(kgK)) at 30 kV/cm and 161 °C deduced from Eq. (7) (Tuttle and
Payne, 1981).
A direct ECE measurement was carried out for (1-x)Pb(Mg
1/3
Nb
2/3
)O
3
-xPbTiO
3
(x=0.08, 0.10,
0.25) ceramics near room temperature using a thermocouple when a dc electric field was
applied (Xiao, Wang, Zhang, Peng, Zhu and Yang, 1998). A temperature change of 1.4 °C
was observed for x=0.08 although at high temperatures (as x increased), this change was
reduced. This high ECE can be accounted for by considering the electric field-induced first-
order phase transition from the mean cubic phase to 3m phase.
These results indicate that the ECE in ceramic and single crystal materials are relatively
small, viz. ΔT<2.5 °C, and ΔS<2.9 J/(kgK), mainly because the breakdown field is low, using
applied electric fields that are less than 3 MV/m. Defects existing in bulk materials cause
early breakdown and empirically the breakdown electric field was inversely proportional to
the material’s thickness. For piezoelectric ceramics, the breakdown field (in kV/cm) is
related to the thickness (in cm) via the relationship, E
b
=27.2t
-0.39
, indicating that thin films
are more appropriate for an ECE study. Additionally, the breakdown field of dielectric
polymers can be several orders of magnitude higher than ceramics, suggesting polar-
polymers are good candidates for ECE investigations.
3.2 ECE in ferroelectric and antiferroelectric thin films
In 2006, Mischenko et al. investigated ECE in sol-gel derived antiferroelectric PbZr
0.95
Ti
0.05
O
3
thin films near the F – P transition temperature. In their study, films with 350 nm thickness
were used to allow for electric fields as high as 48 MV/m. An adiabatic temperature change
of 12 °C was obtained (as deduced from Eq. (7)) at 226 °C, slightly above the phase transition
temperature (222°C) (Mischenko, Zhang, Scott, Whatmore and Mathur, 2006). Both the high
electric field and the high operation temperature near phase transition contribute to the
large ΔT (=TΔS/c
E
). On the other hand, its isothermal entropy change is estimated to be 8
J/(kgK), which is not high compared with magnetic alloys exhibiting giant magnetocaloric
effect (MCE) near room temperature, where ΔS ≥30 J/(kgK) was observed (Provenzano,
Shapiro and Shull, 2004). As stated previously, for high performance refrigerants, a large ΔS
is necessary (Wood and Potter, 1985).

To reduce the operational temperature for large ECE in ceramic thin films, Correia et al.
successfully fabricated PbMg
1/3
Nb
2/3
O
3
-PbTiO
3
thin films with perovskite structure using
PbZr
0.8
Ti
0.2
O
3
seed layer on Pt/Ti/TiO
2
/SiO
2
/Si substrates (Correia, Young, Whatmore,
Scott, Mathur and Zhang, 2009). A temperature change of ΔT=9 K was achieved at 25 °C.
An entropy change of 9.7 J/(kgK) can be deduced. A significant difference for ferroelectric
thin films is that the largest ΔT occurs at 25 °C, near the depolarization temperature (18 °C),
not above the permittivity peak temperature. The large ECE only happens at field heating.
Transitions for stable and metastable polar nanoregions (PNR) to nonpolar regions are
accounted for by observed phenomena. Interactions of PNRs are similar to that between the
dipoles in a glass. The field-induced phase transition has been observed in PMN-PT single
crystals (Lu, Xu and Chen, 2005; Ye and Schmid, 1993). Thermal history has a critical impact
on the field- induced phase transition. Relaxor ferroelectrics are of great interest due to their
Electrocaloric Effect (ECE) in Ferroelectric Polymer Films

105
phase transition temperatures being near or at room temperature. The field induced phase
transition may produce larger polarization, e.g. induced polarization, <P
d
>, which can lead
to larger dP/dT as well as large ΔS and ΔT.
For thin film, the substrate must be taken into account as it may exert stresses on the thin
film due to the misfit of the lattices and electromechanical coupling from the strain changes
under electric field. The free energy of thin film is subject to lateral clamping and may be
expressed as (Akay, Alpay Mantese, and Rossetti Jr, 2007)

106
method). In our study, both the indirect method and direct method were employed to
characterize the ECE in polymer films. The direct comparison of the results from two
methods can also shed light on how reliable the indirect method is in deducing the ECE
from a ferroelectric material.
There are several methods that have been used in measuring the magnetocaloric effect
(MCE) in terms of measuring the isothermal entropy change and adiabatic temperature
change, such as thermocouple (Dinesen, Linderoth and Morup, 2002; Lin, Xu and Zhang,
2004; Spichkin, Derkachb, Tishin, Kuz’min, Chernyshov, Gschneidner Jr, and Pecharsky,
2007), thermometer (Gopal, Chahine and Bose, 1997), and calorimeter (Tocado, Palacios and
Burriel, 2005; Pecharsky, Moorman and Gschneidner, Jr, 1997).
Here, a high resolution calorimeter was used to measure the sample temperature variation
due to ECE when an external electric field was applied (Yao, Ema and Garland, 1998). The
temperature signal was measured by a small bead thermistor. A step-like pulse was
generated by a functional generator to change the applied electric field in the film, and the
width of the pulse was chosen so that the sample can reach thermal equilibrium with
surrounding bath. Due to the fast electric as well as thermal response (ECE) of the polymer
films (in the order of tens of milliseconds (Furukawa, 1989), a simple zero-dimensional
model to describe the thermal process can be applied with sufficient accuracy. In a
relaxation mode, the temperature T(t) of the whole sample system can be measured, which
has an exponential relationship with time, i.e.
( )
/
,
t
bath
T t T Te
τ −
= + Δ (16)
where T
bath
is the initial temperature of the film, ΔT the temperature change of the polymer
film. The total temperature change ΔT
EC
of the whole sample system was measured, which
can be expressed as
i EC
EC p p
T T C /C Δ = Δ
∑
. Here,
i
p
C represents the heat capacity of each
subsystem,
EC
p
C is the heat capacity of the polymer film covered with electrode. ΔT
EC
was
measured as a function of temperature at constant electric field and as a function of electric
field at constant temperature. ΔS can be determined from TΔS=
i
p
C ΔT.
4.2 ECE in the normal ferroelectric P(VDF-TrFE) 55/45 mol% copolymer
4.2.1 Experimental results of ECE
As indicated in Section 2, the ferroelectric copolymer may produce large ECE near its phase
transition temperature. P(VDF-TrFE) 55/45 mol% was chosen because its F-P phase
transition is of second-order (continuous), thus avoiding the thermal hysteresis effect
associated with the first-order phase transition. In addition, among all available P(VDF-
TrFE) copolymers, this composition exhibits the lowest F-P phase transition temperature (~
70 °C), which is favorable for refrigeration near room temperature.
Polymer films used for the indirect ECE measurement were prepared using a spin-casting
method on metalized glass substrates. The film thickness for this study was in the range of
0.4 μm to 1 μm. The free-standing films for the direct ECE measurement were fabricated
using a solution cast method and the film thickness is in the range of 4 μm to 6 μm. Figure 2
shows the permittivity as a function of temperature for P(VDF-TrFE) 55/45 mol%
copolymers measured at 1 kHz. It can be seen that the thermal hysteresis between the
heating and cooling runs is pretty small (~ 1 °C). The remanent polarization as a function of
Electrocaloric Effect (ECE) in Ferroelectric Polymer Films

107
temperature shown in Fig. 3 further indicates a second-order phase transition occurred in
the material. The phase transition temperature is about 70 °C, and the glass transition
temperature is about -20 °C. At temperature higher than 100 °C, the loss tangent rises
sharply, which is associated with the thermally activated conduction.

Fig. 2. Permittivity as a function of temperature for P(VDF-TrFE) 55/45 mol% copolymers.

Fig. 3. Remanent polarization as a function of temperature for P(VDF-TrFE) 55/45 mol%
copolymers.
Figure 4 shows the electric displacement as a function of electric field measured at various
temperatures. At temperatures below the transition temperature, the polymer film is in a
ferroelectric state, the normal hysteresis loop is observed while at higher temperatures, the
loop becomes slimed, remanent polarization diminishes, and saturation polarization still
exists. Hence the electric displacement as a function of electric field at different temperatures
can be procured, which is presented in Fig. 5 (Neese, 2009). One can see that the electric
displacement monotonically decreases with temperature above the phase transition. The
Maxwell relations were used to calculate the isothermal entropy change and adiabatic
temperature change as a function of ambient temperature. The results deduced are
presented in Figs. 6 and 7.
Ferroelectrics

Fig. 6. Isothermal entropy changes as a function of ambient temperature at different electric
fields.

Fig. 7. Adiabatic temperature changes as a function of ambient temperature at different
electric fields.
Present in Fig. 8 is the directly measured ΔS and ΔT as a function of temperature measured
under several electric fields for the unstretched P(VDF-TrFE) 55/45 mol% copolymer. As
can be seen, the ECE effect reaches maximum at the temperature of FE-PE transition. A
comparison between the directly measured and deduced ECE indicates that within the
experimental error, the ECE deduced from the Maxwell relation is consistent with that
directly measured. Therefore, for a ferroelectric material at temperatures above F-P
transition, Maxwell relation can be used to deduce ECE.
4.2.2 Phenomenological calculations on ECE
It is well established by many studies (see Fig. 2) that the F-P phase transition of P(VDF-
TrFE) 55/45 copolymer is of second-order. For the copolymer with 2
nd
order phase
transition, free energy associated with polarization can be written as
( )
2 4
0 c
1 1
G G β T T P ξP EP
2 4
= + − + − (17)
Ferroelectrics

110
where G
0
is the free energy of the material not associated with polarization, β and ξ are
phenomenological coefficients, that are assumed temperature independent. T
c
is the Curie
temperature, E the electric field, and P the polarization.
Differentiating G with respect to P yields the relationship between E and P,
( )
3
c
E β T T P P . ξ = − + (18)
When E=0 and at T<T
c
,

c
1
β(T T )
ε
= −
(T≥Tc). (21)
Using Eqs. (19) and (21), the permittivity versus temperature (Fig. 2), and the polarization
versus temperature relationships (Fig. 3), β and ξ can be obtained. Their values are,
β=2.4×10
7
(JmC
-2
K
-1
), and ξ=3.9×10
11
(Jm
5
C
-4
).
Now Eq. (18) can be used to derive the polarization as a function of temperature under
different DC bias fields. Before doing the calculation, it should be noted that the F-P
transition temperature is a function of DC bias field. This relationship was obtained by
directly measuring the permittivity as a function of temperature in different DC bias fields.
The results are shown in Fig. 9.
However, the dielectric measurement becomes extremely difficult when E
DC
>100 MV/m.
Hence, the relationship of ΔT
c
– E
2/3
(Lines and Glass, 1977) was fitted and extrapolated to
obtain T
c
at E > 100 MV/m.
The calculated polarization versus temperature relationships under different DC biases are
shown in Fig. 10. Based on the D-T data, the ΔS and ΔT can be calculated via Eqs. (6) and (7).
Results are shown in Figs. 11 and 12.

Fig. 12. ECE temperature changes versus temperature for 55/45 copolymer.
Phenomenological calculation indicates that, there is a giant ECE exhibited by P(VDF-TrFE)
55/45 copolymers. The ΔS and ΔT can reach 70 J/(kgK) and 15 °C respectively near the
phase transition temperature ~ 70 °C. It can also be seen that ΔS has a linear relationship
with D
2
(or P
2
), the slope is 1/2β.
4.3 ECE in the relaxor ferroelectric P(VDF-TrFE-CFE) terpolymers
Both the pure relaxor ferroelectric P(VDF-TrFE-CFE) 59.2/33.6/7.2 mol% terpolymer and
blends with 5% and 10% of P(VDF-CTFE) copolymer were studied. For the P(VDF-TrFE-
CFE) relaxor terpolymer, it was observed that blending it with a small amount of P(VDF-
CTFE) 91/9 mol% copolymer [CTFE: chlorotrifluoroethylene] can result in a large increase
in the elastic modulus, especially at temperatures above the room temperature, which does
not affect the polarization level very much. Such an increase in the elastic modulus

114
improves the dielectric strength of the blend polymer films and allows the direct
measurement of ECE to be carried out to higher fields (>100 MV/m).
Present in Fig. 13 is the dielectric constant data for the terpolymer. The D-E loops for the
P(VDF-TrFE-CFE) 59.2/33.6/7.2 mol% terpolymer are presented in Fig. 14, from which ΔS
and ΔT are deduced from the Maxwell relatoin as shown in Fig. 15 (a) and 15 (b),
respectively. The results show that the terpolymer has a weak ECE at room temperature
and increases with temperature. At 55
o
C which is the highest temperature measured, a
ΔS=55 J/(kgK) and ΔT=12 °C under the field of 307 MV/m are deduced from the Maxwell
relation.
The ECE from the direct measurement is presented in Fig. 16, which is for the 59.2/33.6/7.2
mol% terpolymer. The data show quite different behavior compared with Fig. 15. First of
all, the directly measured ECE from the relaxor terpolymer is much larger than that deduced
from the Maxwell relation. Moreover, the directly measured ECE shows much weak
temperature dependence at E < 70 MV/m.

Fig. 16. Directly measured entropy changes (a) and temperature change (b) versus
temperature for 59.2/33.6/7.2 mol% terpolymer .
The results indicate that the Maxwell relation is not suitable for ECE characterization for the
relaxor ferroelectric polymers even at temperatures above the broad dielectric constant
maximum. This is likely caused by the non-ergodic behaviour of relaxor ferroelectric
polymers even at temperatures above the dielectric constant maximum while the Maxwell
relations are valid only for thermodynamically equilibrium systems (ergodic systems)
We also note that a recent report of ECE deduced from the Maxwell relation on a P(VDF-
TrFE-CFE) relaxor ferroelectric terpolymer by Liu et al. (Liu et al. 2010) shows very irregular
field dependence of ECE measured at temperatures below 320 K where ECE in fact
decreases with field, which is apparently not correct. These results all indicate that the
Maxwell relation cannot be used to deduce ECE for the relaxor ferroelectric polymers, or
even the relaxor ferroelectric materials in general, even at temperatures far above the
freezing transition and the broad dielectric constant peak temperature.
5. Conclusions
General considerations for polar materials to achieve larger ECE were presented based on
the phenomenological theory analysis. It is shown that in order to realize large ECE, a
Electrocaloric Effect (ECE) in Ferroelectric Polymer Films

115
dielectric material with a large polarization P as well as large phenomenological coefficient
β is required. It is further shown that both the phenomenological consideration and
experimental data on heat of ferroelectric-paraelectric transition suggest that ferroelectric
P(VDF-TrFE) based polymers have potential to achieve giant ECE. Indeed, experimental
results show that the normal ferroelectric P(VDF-TrFE) 55/45 mol% copolymers exhibit a
large ECE, i.e., an adiabatic temperature change over 12 °C and an isothermal entropy
change over 50 J/(kgK) were obtained. The experimental results also indicate that for the
normal ferroelectric materials, the ECE deduced from the Maxwell relation is consistent
with that directly measured.
The experimental results on ECE in the relaxor ferroelectric P(VDF-TrFE-CFE) terpolymer
were also presented which reveal a very large ECE at ambient condition in the relaxor
terpolymers. In contrast to the normal ferroelectric polymers, the ECE deduced from the
Maxwell relation for the relaxor terpolymers significantly deviates from that directly
measured. The results indicate that the Maxwell relation is not suitable for ECE
characterization for the relaxor ferroelectric polymers even at temperatures above the broad
dielectric constant maximum. This is likely caused by the non-ergodic behaviour of relaxor
ferroelectric polymers even at temperatures above the dielectric constant maximum while
the Maxwell relations are valid only for thermodynamically equilibrium systems (ergodic
systems) .
As a final point, one interesting question to ask when searching for electrocaloric materials
to achieve giant ECE at ambient temperature is how to design dielectric materials to
significantly enhance the entropy in the polar-disordered state since ECE is directly related
to the entropy difference between the polar-disordered and ordered states in a dielectric
material, in other words, how to design a ferroelectric material to increase β while
maintaining large D in Eqs. (9) and (10). This is certainly an interesting area of research. The
successful outcome will have significant impact on the society, in terms of efficient energy
use for refrigeration, new and compact cooling devices which are more environmentally
friendly.
6. Acknowledgements
The works at Penn State University was supported by the US Department of Energy,
Division of Materials Sciences, under Grant No. DE-FG02-07ER46410. The work at Jozef
Stefan Institute was supported by the Slovenian Research Agency. The authors thank B.
Neese, B. Chu, Y. Wang, E. Furman, Xinyu Li, and Lee J. Gorny for their contributions to the
works presented in this chapter.
7. References
Akcay, G.; Alpay, S. P.; Mantese, J. V. & Rossetti Jr., G. A. (2007). Magnitude of the intrinsic
electrocaloric effect in ferroelectric perovskite thin films at high electric fields. Appl
Phys Lett, 90 (25) (JUN, 2007), 252909/1-3. ISSN: 0003-6951.
Amin, A.; Cross, L. E. & Newnham, R. E. (1981). Calorimetric and phenomenological studies of
the PbZrO
3
-PbTiO
3
system. Ferroelectrics, 37 (1-4) (1981), 647-650. ISSN: 0015-0193.
Amin, A; Newnham, R. E.; Cross, L. E. & Cox, D. E. (1981). Phenomenological and structural
study of a low-temperature phase-transition in the PbZrO
3
-PbTiO
3
system. J. Solid
State Chem, 37 (2) (1981), 248-255. ISSN: 0022-4596.
Ferroelectrics

1
University of Electronic Science and Technology of China
2
Huazhong University of Science and Technology
China
1. Introduction
Nowadays, ferroelectric thin films have attracted considerable attention because of their
potential uses in device applications, such as sensors, micro electro-mechanical system
(MEMS) and nonvolatile ferroelectric random access memory (NvFRAM) especially (Scott &
Paz De Araujo, 1989; Paz De Araujo et al., 1995; Park et al. 1999). Lead zirconate titanate
[PbZr
x
Ti
1-x
O
3
(PZT)] ferroelectric thin film is an early material for NvFRAM. PZT and
related ferroelectric thin films, which are most widely investigated, usually have high
remanent polarization (P
r
). However, they are generally suffered from a serious degradation
of ferroelectric properties with polarity switching, when they are deposited on platinum
electrodes.
Bismuth-layered perovskite ferroelectric thin films, with the characteristics of fast switching
speed, high fatigue resistance with metal electrodes, and good retention, have attracted
much attention. Bismuth titanate [Bi
4
Ti
3
O
12
(BIT)] is known to be a typical kind of layer-
structured ferroelectrics with a general formula (Bi
2
O
2
)
2+
(A
m-1
B
m
O
3m+1
)
2-
. Its crystal structure
is characterized by three layers of TiO
6
octahedrons regulary interleaved by (Bi
2
O
2
)
2+
layers.
At room temperature the symmetry of BIT is monoclinic structure with the space group
B1a1, while it can be considered as orthorhombic structure with the lattice constant of the c
axis (c = 3.2843 nm), which is considerably larger than that of the other two axis (a = 0.5445
nm, b = 0.5411 nm). The BIT has a spontaneous polarization in the a-c plane and exhibits two
independently reversible components along the c and a axis (Takenaka & Sanaka, 1980;
Ramesh et al., 1990). It shows spontaneous polarization values of 4 and 50 µC/cm
2
along the
c and a axis respectively. The ferroelectric properties of these bismuth layer-structured thin
films are mostly influenced by the orientation of the films (Simoes et al., 2006). The BIT thin
film is highly c-axis oriented, thus its spontaneous polarization is much lower than that for
a-axis oriented (Fuierer & Li, 2002). For applications in NvFRAM devices, ferroelectric
materials should have high remanent polarization, low coercive field (E
c
), low fatigue rate
and low leakage current density. However, BIT thin film has much lower values of
switching polarization and suffers from poor fatigue endurance and high leakage current as
a result of the internal defects (Uchida et al., 2002). Numerous works have been made to
substitute BIT thin film with proper ions to optimize the ferroelectric properties.
In recent years, it was reported that some A-site or B-site substituted BIT showed large
remanent polarizations. In the case of A-site substitution in BIT, La-substituted BIT
Ferroelectrics

120
[Bi
3.25
La
0.75
Ti
3
O
12
(BLT)] films exhibited enhanced P
r
of 12 µC/cm
2
with high fatigue
resistance, which make them applicable to direct commercialization (Chon et al., 2002).
Other lanthanides ions, such as Nd
3+
, Pr
3+
, Sm
3+
, etc. result in similar results (Watanabe et
al., 2005; Chon et al., 2003; Chen et al., 2004). In the case of B-site substitution in BIT, some
donor ions such as V
5+
, Nd
5+
, W
6+
, could effectively decrease the space charge density
resulting in the improvement of the ferroelectric properties (Kim et al., 2002; Wang &
Ishiwara, 2003). For further improvement of the ferroelectric properties, A and B-site
cosubstitution by various ions should be considered because the properties of BIT based
materials strongly depend on species of the substituent ions.
In this chapter, we first summarized the researches on the effect of A-site or/and B-site
substitution on microstructures and properties of Bi
4
Ti
3
O
12
ferroelectric thin films. Then
La/V substituted BIT thin films were deposited by sol-gel method, and the effect of
substitution of La
3+
and V
5+
on structural and electrical properties of the BIT thin film was
investigated.
2. A-site or B-site substitution
2.1 A-site substitution
The properties of different A-site substituted BIT thin films were summarized in Table 1.
La-substituted BIT (BLT) films exhibited large P
r
and low E
c
with high fatigue resistance,
and BLT thin film has been already applied in commercial NvFRAM product in all A-site
substituted BIT thin films.

films increase monotonously with La content x from x=0-0.6. The fitted lines (assumed for
x>0.6), with different positive slopes, indicated different enlargements in a, b and c and an
increase in cell volume. The increase in the a, b and c lattice paramenters approached single
crystal values with increasing x, which also lowered the orthorhombic distortion, i.e., 2(a-
b)/(a+b). This strongly suggested that the relaxations of structural distortion and strain arise
from the La substitution, which also enhanced P
r
.
Lee et al. (Lee et al. 2002) reported correlation between internal stress and ferroelectric
fatigeue in La-substituted BIT films. When the La content exceeded x=0.25, there was little
change in the chemical stability of elements. Chemical stability of oxygen ions alone could
not fully explain the effect of La substitution on fatigue. The decrease of the strain was
saturated at a composition of x=0.75, and films showed fatigue-free characteristics with this
composition. Thus, internal strain as well as chemical stability of ions play a significant role
in the fatigue behavior of BLT films.
2.2 B-site substitution
The properties of different B-site substituted BIT thin films were summarized in Table 2
(Choi et al., 2004).

Table 2. Summary of the properties of different B-site substituted BIT thin films
Either A-site or B-site substitution can improve remanent polarization of BIT thin film, but
the mechanism is different with each other, and the effect of A-site substitution is
prominent. For A-site substitution, there is a highly asymmetric double-well potential at
TiO
6
octahedro unit adjacent to the interleaving Bi
2
O
2
layer along the c axis, and it results in
the development of remanent polarization along the c axis. For B-site substitution, the
decreasing c-axis orientation results in the development of remanent polarization.
Simultaneously, the role of A-site substitution is to suppress the A-site vacancies
accompanied with oxygen vacancies which act as space charge. And the role of B-site
substitution is the compensation for the defects, which cause a fatigue phenomenon and
strong domain pinning. For further improvement of the ferroelectric properties, A and B-site
cosubstitution by various ions should be considered because the properties of BIT based
materials strongly depend on species of the substituent ions.
Ferroelectrics

122
3. La/V substitution
3.1 Experimental
The BIT, Bi
3.25
La
0.75
Ti
3
O
12
(BLT), Bi
4-x/3
Ti
3-x
V
x
O
12
(BTV) and La
3+
/V
5+
cosubstituted BIT
[Bi
3.25-x/3
La
0.75
Ti
3-x
V
x
O
12
(BLTV)] thin films were prepared on the Pt/TiO
2
/SiO
2
/p-Si(100)
substrates by sol-gel processes. The sol-gel method is one of the chemical solution
deposition (CSD) methods, which is commonly used as a fabrication method for thin films.
The important advantages of sol-gel method are high purity, good homogeneity, lower
processing temperatures, precise composition control of the deposition of multicomponent
compoudns, versatile shaping, and deposition with simple and cheap apparatus.
The precursor solution for these films were prepared from Bismuth nitrate [Bi(NO
3
)
3
•5H
2
O],
lanthanum nitrate [La(NO
3
)
3
•xH
2
O], titanium butoxide [Ti(OC
4
H
9
)
4
] and vanadium
oxytripropoxide [VO(C
3
H
7
O)
3
]. The bismuth nitrate and lanthanum nitrate were dissolved
in 2-methoxyethanol at room temperature to reach clear solution. Titanium butoxide and
vanadium oxytripropoxide were stabilized by acetylacetone at room temperature, which
was also act as the stabilizer. These related solutions were mixed, then sonicated and
refluxed to dissolve the solutes sufficiently and improved the stability of the solutions. The
final concentration in these mixed solutions was adjusted to 0.1 mol/L, and the solutions
were aged in vessels for 24 h to get the BIT, BLT, BTV and BLTV precursors. A 10 mol%
excess amount of bisumth nitrate was used to compensate Bi evaporation during the heat
treatment. The precursor solutions were spin-coated on the Pt/TiO
2
/SiO
2
/p-Si(100)
substrates at 3700rpm for 30 s. Then the sol films were dried at 300
o
C for 5 min and
pyrolyzed at 400
o
C for 10 min to remove residual organic compounds. These processes were
repeated six times to achieve the desired film thickness. Then the films were annealed at
750
o
C for 30 min under air ambient in a horizontal quartz-tube furnace to produce the
layered-perovskite phase.
The phase identification, crystalline orientation, and degree of crystallinity of the prepared
films were studied by a χ' Pert PRO X-ray diffractometer (PANalytical, B V Co., Holland)
with Cu-Ka radiation at 40 kV. The surface and cross-section morphologies were
investigated using a Sirion 200 field-emission scanning electron microscope (FEI Co.,
Holland). The local microstructure and local symmetry of the films were also characterized
by Raman spectroscopy (LabRam HR800, Horiba Jobin Yvon Co., France). The Raman
measurements were performed at room temperature using the 514.5 nm line of an argon ion
laser as the excitation source. Pt top electrodes with an area of about 7×10
-4
cm
2
were
deposited by means of sputtering using a shadow mask for electrical measurements. The
polarization-voltage (P-V) hysteresis loops and fatigue of the films were measured by using
a RT66A ferroelectric test system (Radiant Technology Inc., USA), and the leakage current
behaviors of the films were analyzed using a Keithley 2400 sourceMeter/High Resistance
Meter (Keithley Instruments Inc., USA) with a staircase dc-bias mode and appropriate delay
time at each voltage step.
3.2 The effect of La/V substitution
The XRD patterns of the BIT, BLT, BTV (x=0.03) BLTV (x=0.03) thin films deposited on the
Pt/TiO
2
/SiO
2
/p-Si(100) substrates are shown in Fig. 1. All the diffraction peaks of these film
samples can be indexed according to the reference pattern of Bi
4
Ti
3
O
12
powder [BIT, JCPDS
(Joint Committee on Powder Diffraction Standards) 35-795]. The good agreement in XRD
peaks of the BLT, BTV and BLTV films with those of BIT indicates that the lattice structure
Study on Substitution Effect of Bi
4
Ti
3
O
12
Ferroelectric Thin Films

123
of these films are similar to that of BIT. It can be seen that all the films are the single phase of
layer-structured perovskite and no pyrochlore phase. The BIT film exhibits a high c-axis
orientation with the (00l) peak being of highest intensities, while the BLTV film exhibits a
highly random orientation with the (117) peak being of highest intensity. In order to
determine the degree of preferred orientation, the volume fraction of c-axis-oriented grains
in a film sample is defined as

* *
(00 ) 00 00
( / ) / ( / )
l n n hkl hkl
I I I I α = ∑ ∑ (1)
Where
hkl
I is the measured intensity of (hkl) for the films,
*
hkl
I is the intensity for powders, and
n is the number of reflections (Lu et al., 2005; Bae et al., 2005). The α values obtained for the
BIT, BLT, BTV BLTV films corresponding to Fig. 1 are 76.4, 46.1, 52.5 and 24.4% respectively.
The BIT film shows c-axis preferred orientation, other films show random orientation.

Fig. 1. XRD patterns of the BIT, BLT, BTV and BLTV thin films deposited on the
Pt/TiO
2
/SiO
2
/p-Si(100) substrates
The BIT film has a strong tabular habit with the growth of c-axis orientation, for the energy
of the (00l) surfaces is lower and consequently the (h00) and (0k0) faces grow more rapidly.
Yau et al. (Yau et al. 2005) reported that, for La-substituted BIT thin films (Bi
4-x
La
x
Ti
3
O
12
), the
degree of c-axis orientation decreases with the increase of La content x (Yau et al., 2005).
Choi et al. reported that, for B-site(V
5+
, W
6+
, Nb
5+
) substituted BIT thin films, the degree of c-
axis orientation decreases greatly with different donor ions substitution (Choi et al., 2004).
The substitution may break down the Ti-O chains due to the differences in the electron
affinites, which results in the clusters in the precursor favoring the growth of non-c-axis
orientation. Thus, the BLT, BTV and BLTV thin films with substitition exhibit less highly c-
axis oriented than the typical unsubstituted BIT thin film, and the result suggests that
substitution has an important effect on the orientation of the BIT films.
The lattice constants of the four different film samples are also influenced by the
substitution. The lattice constans have been calculated from the XRD patterns and listed in
Ferroelectrics

124
Table 3. The lattice constant, a, decreases and b increases as La
3+
is substituted, while a
increases and b decreases as V
5+
is substituted. The orthorhombicity could reflect the
variation in the lattice constants, which is defined as 2(a-b)/(a+b). The variation of
orthorhombicity agrees well with those reported in the literature for La-substituted
Bi
4
Ti
3
O
12
. The decrease of orthorhombicity for the BLT film suggests relaxation of the
structural distortion, while the increase for the BTV and BLTV films suggests a increase of
the structural distortion and a decrease of the symmetry.

125
Figure 2 shows the field-emission scanning electron microscopy (FE-SEM) surface and cross-
section morphologies of these thin films. All the films show dense microstructure without
any crack. The thickness of the films is about 360 nm by the cross-section view. From the
surface morphologies, it can be seen that the BLTV film is mainly composed of fine rod-like
grains with small sizes about 80-160 nm in Fig. 2(d), while the BIT film is mainly composed
of large or small plate-like grains with sizes up to 200-500 nm in Fig. 2(a). And it also can
been found from the cross-section micrographs, the rod-like grains for the BLTV film slant
toward to the film surface in Fig. 2(f), while the large columnar grains for the BIT film are
vertical to the film surface in Fig. 2(e). The rod-like grains increase and plate-like grains
decrease in the BIT films after substitution of La
3+
or V
5+
, and also the size of plate-like
grains decreases. For BIT based films, the rod-like grains are related to the growth of
random orientation and the plate-like grains are related to the growth of c-axis orientation
(Lee et al., 2002; Li et al.,2007). In Fig. 1, we can see that the full-width at falf-maximum
(FWHM) of the (00l) peak decreases after substitution of La
3+
or V
5+
, which indicates the
restricted growth of (00l)-oriented grains. So the results of FE-SEM surface and cross-section
morphologies agree with those of the XRD patterns discussed above.
Raman scattering is a powerful probe in studying complex-structured materials because it is
highly sensitive to local microstructure and symmetry. The Raman spectra for these films
were investigated in the Raman frequency shift range of 100-1000 cm
-1
as presented in Fig. 3.
For bismuth layer-structured ferroelectrics (BLSFs), their phonon modes can generally be
classified into two categories: low frequency modes below 200 cm
-1
and high frequency
modes above 200 cm
-1
(Shulman et al., 2000). The low frequency modes below 200 cm
-1
are
related to large atomic masses, which reflect the vibration of Bi
3+
ions in (Bi
2
O
2
)
2+
layer and
A-Site Bi
3+
ions. The high frequency modes above 200 cm-1 reflect the vibration of Ti
4+
and
TiO
6
octahedron. The phonon modes at 118 and 147 cm
-1
reflect the vibration of A-site Bi
3+

ions in layer-structured perovskite. These modes shift to higher frequencies in the BLT and
BLTV films after A-site La
3+
substitution, but almost remain unchanged in the BTV film after
B-site V
5+
substitution, which suggests the B-site V
5+
substitution has not affected the A-site
Bi
3+
ion. The average masses of La/Bi decrease for La atomic mass is lower than Bi atomic
mass (M
La
/M
Bi
=139/208), so the related modes show high-frequency shift, which also
indicates A-site Bi
3+
ions in BIT film are partly substituted for La
3+
.
The 231 and 270 cm
-1
modes are considered to reflect the distortion modes of TiO
6

octahedron. The 231 cm
-1
mode is Raman inactive when the symmetry of the TiO
6

octahedron is O
h
, but it becomes Raman active when distortion occurs in TiO
6
octahedron.
The disappearance of the 231 cm
-1
mode and low-frequency shift of 270 cm
-1
mode for the
BLT film could be explained by a decrease in distortion of TiO
6
due to the influence of La
3+

ions substitution which may lower the corresponding binding strength and decrease the
Raman shift (Zhu et al., 2005). And it is consistent with the decrease of orthorhombicity for
the BLT film. While in B-site V
5+
substituted BTV film, the 231 cm
-1
mode almost remains
unchanged and 270 cm
-1
mode shifts to a slightly higher frequency. These results suggest
that the A-site La
3+
substitution has influenced the B-site Ti
4+
ions in TiO
6
octahedron.
The 537 and 565 cm
-1
modes are attributed to a combination of stretching and bending of
TiO
6
octahedron in BIT. According to references, A-site La
3+
substitution leads to structural
disorder and in turn broadens the line of these two modes, thus resulting in the mode at 557
cm
-1
in the BLT and BLTV films (Wu et al., 2001). The only B-site V
5+
substitution in the BTV
film does not affect these two original modes greatly with both shifting to slightly higher
Ferroelectrics

126
frequencies. Thus the variation of the mode frequencies at 537, 557 and 565 cm
-1
also implies
that the A-site La
3+
substitution exerts influence on Ti
4+
ions in B sites of the BIT thin film.

substitution in the BTV film results in its significant low-frequency shift, indicating that the
V
5+
is entering into the lattice replacing the Ti
4+
in B site and a decrease in O
h
symmetry of
TiO
6
octahedron, which is consistent with the increase of orthorhombicity for the BTV film.
The wave number of the mode of the BLTV film is between the corresponding one of the
BLT and BTV films, which should be attributed to the effects of cosubstitution of La
3+
and
V
5+
in A and B sites, respectively. On the other hand, for the BLTV film, since V
5+
is
electronically more active than Ti
4+
, and there is a little asymmetry of TiO
6
, a increase in Ti-
O hybridization is implied.
Figure 4 shows the P-V curves of the BIT, BLT, BTV and BLTV thin film capacitors at a
voltage of 12 V. The only B-site V
5+
substitution improves the ferroelectric properties of BIT
film slightly. The BLT and BLTV films show well-saturated hystersis loops. The measured
values of 2P
r
and 2E
c
are 15.6 µC/cm
2
and 248 kV/cm for the BIT film, 37.6 µC/cm
2
and 226
kV/cm for the BLT film, 21.6 µC/cm
2
and 188 kV/cm for the BTV film, 50.8 µC/cm
2
and 194
kV/cm for the BLTV film, respectively. For A-site substituted BIT film, the E
c
usually varys
slightly, while for B-site substituted BIT film, the E
c
becomes smaller (Wang & Ishiwara,
2002). All these substitutions can improve the P
r
value for the BIT film, and the BLTV film
has the largest P
r
with smaller E
c
among these films. On one hand, the spontaneous
polarization of BIT along the c-axis is know to be much smaller than that along the a-axis.
From this viewpoint, randomly oriented films are considered to be more favorable than c-
axis oriented films. Therefore the randomly oriented BLTV and BLT films have a more
Study on Substitution Effect of Bi
4
Ti
3
O
12
Ferroelectric Thin Films

127
suitable orientation in comparison with other film samples for achieving large P
r
. And the
BLTV film gets the largest P
r
for its least degree of c-axis orientation. On the other hand, as
hybridization is essential to ferroelectricity, the increase of hybridization may increase the
polarization (Cohen, 1992). Thus the increase of Ti-O hybridization inside TiO
6
of the BLTV
film results in its excellent ferroelectric properties.

Fig. 4. Polarization-voltage (P-V) hysteresis loops of the BIT, BLT, BTV and BLTV thin films
at the voltage of 12 V
Figure 5 illustrates the fatigue characteristics of these thin films. The test was performed at
room temperature using 12 V, 100 kHz bipolar square pulses. From the figure we can see
that, as the switching cycles increase, the normalized P
r
(the P
r
to the initial polarization) of
the BLT, BTV and BLTV films decreases silghtly, while that of the BIT film decreases greatly.
The P
r
of the BIT, BLT, BTV and BLTV films decreases by 24%, 14%, 16% and 10%
respectively after 10
10
cycles.
The strongest fatigue endurance for the BLTV film and good fatigue property for the BLT
and BTV films after La
3+
and V
5+
substitution are due to the decrease of the defects, such as
oxygen vacancies. For BLSF materials, some oxygen vacancies and Bi vacancies are
generated unavoidably because of the volatilization of Bi during the annealing processes
under high temperatures (Yuan & Or, 2006). The reaction mechanism is as follow:

128
atoms is helpful to the fatigue behavior (Kang et al., 1999). For the BTV and BLTV films, V
5+

substitution for Ti
4+
and a decrease in Bi content are conducted simultaneously to maintain
the charge neutrality, as indicated by the equation of composition (Bi
4-x/3
Ti
3-x
V
x
O
12
and Bi
3.25-
x/3
La
0.75
Ti
3-x
V
x
O
12
). Furthermore, the substitution of the B-site Ti
4+
for the donor-type V
5+
can
suppress the generation of oxygen vacancies due to the charge neutrality restriction (Sun et
al., 2006). The reaction mechanisms are as follows:

.
2 5
2 5 2
Ti O
V O V O e′ ↔ + + (3)

..
2
1
2
2
o O
O e O ν ′ + + ↔ (4)

.
3 3
Bi Ti Bi Ti
Bi V Bi V ν′′′ + + ↔ + (5)
where
.
Ti
V is the V ion with +1 effective charge at the Ti site,
Ti
V is the V at the Ti,
O
O is
oxide in the lattice,
Bi
Bi is Bi in the lattice, and e is the compensatory charge. Thus,
Bi
ν′′′ , the
tervalent negative electric center, is neutralized by
.
Ti
V , and the oxygen vacancies are
suppressed by the higher-valentcation substitution. So the substitution of A-site La
3+
and B-
site V
5+
in BIT thin film can improve the properties of the ferroelectric thin film effectively.
The BLT and BTV thin films show good fatigue properties.

Fig. 5. Fatigue characteristics of the BIT, BLT, BTV and BLTV thin films
The volatile Bi is partly substituted for La, and there are still Bi and oxygen vacancies. There
are small amounts of V
5+
substitution in the present BLTV film, which could avoid more
charge defects caused by excessive V
5+
substitution according to equation (3). The decrease
of oxygen vacancies still follows the proposed equation (4) in the BLTV film except for the
effect of La
3+
substitution. The decrease and suppression of oxygen vacancies are enhanced
Study on Substitution Effect of Bi
4
Ti
3
O
12
Ferroelectric Thin Films

129
by simultaneous substitutions of La
3+
and V
5+
in the BLTV film. Thus, cosubstitution of La
3+

and V
5+
in the BLTV film results in its excellent fatigue property.
The dc leakage current is usually one of the most concerned factors for NvFRAM
application of ferroelectric thin films, because of its direct relation to power consumption
and function failure of devices (Araujo et al., 1990). Therefore leakage current measuremnts
are a crucial part of any electrical characterization. During the measurement, the dc voltage
over a range of 0-5 V was applied with a step of 0.05 V, and a delay time of 10 s between
each step to ensure the collected data of steady state. The leakage current characteristics of
current density (J) versus electric field (E) for these thin films at room temperature are
shown in Fig. 6. The leakage current density increases gradually at low electric field, but
generally in the order of 10
-9
-10
-8
A/cm
2
for the BLTV film, 10
-8
-10
-7
A/cm
2
for the BLT and
BTV films, and 10
-6
-10
-5
A/cm
2
for the BIT film below 100 kV/cm. The leakage current
density of the BLT and BTV films is smaller than that of the BIT film, and the BLTV film
acquires the smallest leakage current density.

Fig. 6. Electric field dependence of leakage current density for the BIT, BLT, BTV and BLTV
thin films
For further study of the effect of La
3+
and V
5+
cosubstitution, the leakage current behaviors
for the BIT and BLTV films were measured at various temperatures from 20 to 150
o
C in Fig.
7. The mechanisms of leakage currents are closely related to the temperature for the
thermally assisted conduction process. There is a systematic increase in leakage current
density with the increase in temperature for both of the films, but the leakage current
density for the BIT film increases faster with the increase of the voltage and temperature.
Figs 7 (c) and (d) show the plots of log J versus log E of the films in the temperature range
from 20 to 150
o
C. In the low electric field region, the leakage current shows an ohmic
behavior with the slope of log J/log E being about 1. The linear region extends up to a onset
voltage, at which the space charges start dominating the conduction process. The onset
voltage decreases with the increase of the temperature, which is seen from the figures. In the
Ferroelectrics

130
high electric field region, the slope is varying from 2.16 to 2.30 for the BLTV film with the
increase of the temperature, while 2.28 to 2.72 for the BIT film, which agrees with the space
charge limited current (SCLC) leakage mechanism for both of the films. The larger slop for
the BIT film could be caused by more thermally excited electrons from trap levels in the film
(Chaudhun & Krupanidhi, 2005). Both electrons and oxygen vacancies domain the space
charge mechanism. At low temperatures, oxygen vacancies somehow do not respond to the
high electric field, and the highly mobile electrons are the major charge carriers of the
current. However, oxygen vacancies play a significant role in the space charge mechanism at
high temperatures (Bhattacharyya et al., 2002). From Figs 7 (c) and (d), we can see that the
leakage current density increases in three order of magnitude for the BIT film in the high
electric field at 150
o
C(when the temperature was increased from 20 to 150
o
C), while
increases in less than one order of magnitude for the BLTV film. For there are more oxygen
vacancies in the BIT film, the leakage current density for the film increases drastically in the
high electric field at the high temperature. Therefore, the improved leakage current property
is also attributed to the decrease and suppression of oxygen vacancies after La
3+
and V
5+

131
3.3 The Effect of V content in BLTV
To acquire the optimal content of V substitutition, Bi
3.25-x/3
La
0.75
Ti
3-x
V
x
O
12
were prepared
with different content of V substitutition (x: 0-8%) by sol-gel processes.
The XRD patterns of the BLT, BLTV(x=1%, 3%, 5%, 8%) thin films deposited on the
Pt/TiO
2
/SiO
2
/p-Si(100) substrates are shown in Fig. 8. It can be seen that increasing V
content do not destroy their crystal structure and all the films are the layered perovskite
structure. The BLT film without V substitution exhibits higher intensity of (006) peak. The
intensity of this peak decreases with V content increasing from 0 to 0.05, but increases again
when V content increasing to 0.08. The volume fraction of c-axis-oriented grains in BLTV
x

(0-8%) films calculated according to equation (1) is 31.7, 21.5, 16.9, 20.8 and 39.3 respectively.
Thus, the BLTV(3%) film shows the least degree of c-axis orientation.

Fig. 8. XRD patterns of the BLTV(x: 0-8%) thin films deposited on the Pt/TiO
2
/SiO
2
/p-
Si(100) substrates
Figure 9 shows the FE-SEM surface and cross-section morphologies of the BLTV(x: 0-8%)
thin films. All the films show dense microstructure without any crack. From the surface
morphologies, it can be seen that the BLT film is mainly composed of fine rod-like and plate-
like grains. The rod-like grains increase but the plate-like grains decrease with V content
increasing, and there are most rod-like grains when V content is 3% and 5%. Whereas, plate-
like grains increase again when V content increasing to 8%. The result of FE-SEM surface
morphologies agrees with that of the XRD patterns discussed above.
The Raman spectra for these BLTV(x: 0-8%) thin films were investigated in the Raman
frequency shift range of 100-1000 cm
-1
as presented in Fig. 10. The 852 cm
-1
mode is a pure
stretching of TiO
6
octahedron, Raman shift for BLTV(1%), BLTV(3%), BLTV(5%) and
BLTV(8%) thin films is 851, 850, 850 and 848 cm
-1
respectively at this mode. There are two
obvious peaks between 600 and 800 cm
-1
mode for BLTV(8%) thin film, which indicates a great
increase of the structural distortion and a great decrease in O
h
symmetry of TiO
6
octahedron.
Ferroelectrics

133
Figure 11 shows the P-V curves of these BLTV(x: 0-8%) thin film capacitors at a voltage of 12
V. All these thin films show well-saturated hystersis loops. With increasing of substitution
content, P
r
increases. In the range x>3%, P
r
decreases with increasing V content. When
x=8%, P
r
becomes lower than that of BLT and the squareness of the hystersis loop is
degraded as well.

Fig. 12. P
r
and E
c
of the BLTV(x: 0-8%) thin films as functions of the V content
Ferroelectrics

134
Figure 12 summarizes the variation in the P
r
and E
c
against the V content in the BLTV(x: 0-
8%) thin films. The P
r
values under the voltage of 12 V were 18.8, 20.1, 25.4, 22.1 and 13.2
μC/cm
2
, respectively, for x = 0, 1%, 3%, 5%, 8%. The BLTV(3%) thin film gets the largest P
r

for its least degree of c-axis orientation. On the other hand, as hybridization is essential to
ferroelectricity, the increase of hybridization may increase the polarization. Thus the
increase of Ti-O hybridization inside TiO
6
of the BLTV(3%) thin film results in its excellent
ferroelectric properties. After the substitution content is above 5%, P
r
begins to decrease, this
is because of a limited solution of V ion in BLTV thin films. The great increase of the
structural distortion results in a great decrease of ferroelectric properties.
Figure 13 illustrates the fatigue characteristics of these BLTV(x: 0-8%) thin films. With
increasing of substitution content, the fatigue property is improved. In the range x>3%, the
fatigue property is worsened with increasing V content. Small amounts of V
5+
substitution
can suppress the generation of oxygen vacancies due to the charge neutrality restriction, but
excessive V
5+
substitution will cause more charge defects which worsen the fatigue
property.

135
from the FE-SEM surface and cross-section morphologies. Raman spectra show the A-site
La
3+
substitution exerts influence on Ti
4+
ions in B sites of the BIT thin film, TiO
6
(or VO
6
)
symmetry decreases and Ti-O (or V-O) hybridization increase for V
5+
substitution. Either A-
site La
3+
or B-site V
5+
substitution can improve the P
r
value for the BIT thin film, but only the
BLT and BLTV film capacitors are characterized by well-saturated P-V curves at an applied
voltage of 12 V. The BLTV thin film shows the largest 2P
r
of 50.8 µC/cm
2
with small 2E
c
of
194 kV/cm among these films. For the BLTV thin film, the fatigue test exhibits the strongest
fatigue endurance up to 10
10
cycles and the leakage current density is generally in the order
of 10
-9
-10
-8
A/cm
2
below 100 kV/cm at room temperature while increasing in less than one
order of magnitude at the temperature range from 20 to 150
o
C. To acquire the optimal
concentration of V substitutition, BLTV were prepared with different concentration of V
substitutition (x: 0-8%). The remanent polarization and fatigue properties first increase then
decrease with increasing of V content. BLTV(3%) thin film exhibits excellent ferroelectric
property and the strongest fatigue endurance up to 10
10
cycles. When V content increases to
8%, the properties decrease due to slightly large distortion of crystal lattice and charge
defects caused by excessive V substitution. The excellent properties of the BLTV thin film
are attributed to the effective decrease or suppression of oxygen vacancies after La
3+
and V
5+

138
Zhu, J.; Chen, X. B.; Zhang, Z. P. & Shen, J. C. (2005). Raman and X-ray photoelectron
scattering study of lanthanum-doped strontium bismuth titanate. Acta. Mater., Vol.
53, No. 11, pp. 3155-3162, ISSN 1359-6454
8
Uniaxially Aligned Poly(p-phenylene vinylene)
and Carbon Nanofiber Yarns through
Electrospinning of a Precursor
Hidenori Okuzaki and Hu Yan
University of Yamanashi
Japan
1. Introduction
Nanofibers made of conducting or semiconducting polymers have been extensively studied
from both fundamental and technological aspects to understand their intrinsic electrical and
mechanical properties and practical use for elecctromagnetic interference shielding,
conducting textiles, and applications to high-sensitive sensors and fast-responsive actuators
utilizing their high speccific surface area (Okuzaki, 2006).
Poly(p-phenylene vinylene) (PPV) has been paid considerable attention due to its properties
of electrical conductivity, electro- or photoluminescence, and non-linear optical response,
which have potential applications in electrical and optical devices, such as light-emitting
diodes (Burrourghes et al., 1991), solar cells (Sariciftci et al., 1993), and field-effect transistors
(Geens et al., 2001). Most of the work with regard to PPV exploits thin coatings or cast films
(Okuzaki et al., 1999), while a few reports have been investigated on PPV nanofibers by
chemical vapor deposition polymerization with nanoporous templates (Kim & Jin, 2001).
The electrospinning, a simple, rapid, inexpensive, and template-free method, capable of
producing submicron to nanometer scale fibers is applied to fabricate nanofibers of
conducting polymers, such as sulphuric acid-doped polyaniline (Reneker & Chun, 1996) or a
blend of camphorsulfonic acid-doped polyaniline and poly(ethylene oxide) (MacDiarmid et
al., 2001). However, the electrospinning is not applicable to PPV because of its insoluble and
infusible nature. Although poly[2-methoxy-5-(2’-ethylhexyloxy)-1,4-phenylenevinylene], an
electro-luminescent derivative of PPV, could be electrospun from 1,2-dichloroethane
solution as a randomly oriented mesh, the resulting fibers were not uniform exhibiting leaf-
like or ribbon-like morphology due to the low viscosity limited by the polymer solubility
(Madhugiri et al., 2003).
On the other hand, carbon nanofibers have superior mechanical properties, electrical
conductivity, and large specific surface area, which are promising for various potential
applications in nanocomposites such as electromagnetic interference shielding (Yang et al.,
2005), rechargeable batteries (Kim et al., 2006), and supercapacitors (Kim et al., 2004).
Currently, the carbon nanofibers are fabricated by a traditional vapor growth (Endo, 1988),
arc discharge (Iijima, 1991), laser ablation, and chemical vapor deposition (Ren et al., 1998),
but they involve complicated processes and high equipment costs for the fabrication.
Reneker et al. fabricated carbon nanofibers by carbonization of electrospun polyacrylonitrile
Ferroelectrics

140
(PAN) precursor fibers (Chun et al., 1999). Carbon nanofibers can also be derived from
various precursors, such as mesophase-pitch (Park et al., 2003), polybenzimidazol (Kim et
al., 2004), and polyimide (Chung et al., 2005). The electrospun fibers are, however, directly
deposited on the grounded target as a randomly oriented mesh.
This chapeter deals with a successful fabrication of uniaxially aligned PPV and carbon
nanofibers by electrospinning of a soluble precursor and subsequent thermal conversion or
carbonization (Fig. 1). The effects of spinning and carbonization conditions on morphology
and structure of the resulting nanofiber yarns have been investigated by means of scanning
electron microscopy (SEM), Fourier transform infrared (FT-IR), wide-angle X-ray diffraction
(WAXD), thermogravimetry (TG), and Raman analyses.

Fig. 1. Flow chart for fabrication of conducting PPV and carbon nanofiber yarns.
2. Experimental
Poly(p-xylenetetrahydrothiophenium chloride) (PXTC), a precursor of PPV, was
commercially available in the form of 0.25% aqueous solution from Aldrich Inc. The M
w

determined by membrane osmometry was 1.3 x 10
5
, while low-angle laser-light scattering
combined with centrifugation yielded M
w
= 9.9 x 10
5
(M
n
= 5.0 x 10
5
, M
w
/M
n
= 2.0) (Gagnon
et al., 2006). About 1 ml of PXTC solution containing different amount of methanol was
poured into a glass syringe (12 mm in diameter) and an electric field was applied to a single-
hole spinneret (340 µm in diameter) from a variable high-voltage power supply (Towa
Keisoku) capable of applying positive voltages (E) up to 30 kV. The electrospun fibers were
collected on a grounded flat plate (10 x 10 cm) covered with an aluminum foil used as a
target where the distance between the needle and the target electrode was 20 cm. The
viscosity of the PXTC solution was measured at 30 °C with a B-type viscometer (VM-10A,
CBC Materials). The diameter of yarn was measured with an optical microscope equipped
with a video system (InfiniTube, Edmund Optics). The thermogravimetric (TG) analysis was
performed with a TG-DTA (2000S, MAC Science) in a temperature range from room
temperature to 1000 °C at a heating rate of 10 °C min
-1
under an argon atmosphere. The
PXTC yarns were subsequently converted to PPV yarns by heat treatment at 250 °C for 12 h
in vacuum. FT-IR spectra was measured with a FTIR-8100 (Shimadzu) and wide-angle X-ray
Uniaxially Aligned Poly(p-phenylene vinylene)
and Carbon Nanofiber Yarns through Electrospinning of a Precursor

141
diffraction patterns were measured with a RINT (Rigaku). Carbonization of the PXTC yarns
was carried out in a quartz tube under vacuum by using an electric furnace (FR100,
Yamato). The diameter of thus-carbonized fiber was measured with an FE-SEM (S-4500,
Hitachi) and the distribution was evaluated by measuring at least 100 points. The Raman
spectra were measured with a laser Raman spectrometer (NRS-2100, JASCO) equipped with
an optical microscope. Excitation light from an argon ion laser (514.5 nm) was focused on
the fiber surfaces through the optical microscope.
3. Results and discussion
3.1 Spontaneous formation of PXTC yarns by electrospinning
Fig. 2 shows optical images of PXTC yarns spontaneously formed by electrospinning at C =
0.1% and E = 20 kV). When the applied voltage reaches a critical value, the electrostatic force
overcomes the surface tension of the PXTC solution, thereby ejecting a jet from the
spinneret.

142
Since the PXTC chains and solvent molecules bear the same (positive) charge, they repel
each other and the droplets become smaller due to the separation while traveling in air
during a few milliseconds from the spinneret to the grounded target. Meanwhile,
evaporation of solvent molecules takes place rapidly because the separation of droplets
produces high surface area to volume. Conventionally electrospun fibers are directly
deposited on the grounded target as a randomly oriented mesh due to the bending
instability of the highly charged jet. In contrast, the PXTC is electrospun into centimeters-
long yarns vertically on the surface of the aluminum target but parallelly to the electric field
where an electrostatic attractive force stretches the yarn vertically on the target electrode,
leading to a successive upward growth of the yarn. It should be noted that a few yarns get
twisted while swinging due to the bending instability of the jet and grow into a thicker yarn.
The unusual formation of the yarns can be explained by the ionic conduction of the PXTC
(Okuzaki et al., 2006), i. e., the deposited PXTC fibers discharge through polyelectrolyte
chains to the ground target, which prefers the following deposition on the electrospun fibers
so as to decrease the gap between the fibers and the spinneret. Once a yarn forms by
touching the adjacent fibers, the following deposition may preferably occur on the yarn
rather than on the individual fibers because of the low electric resistance.

Fig. 3. Effects of applied voltage and concentration on formation of PXTC yarns at various
relative humidities.
In order to clarify the mechanism of the yarn formation in more detail, electrospinning was
performed at various relative humidities (RHs) and the results were shown in Fig. 3. At 30
%RH, yarn formed only in a area of C = 0.075~0.125% and E = 15~30 kV, while at 70 %RH
the area expanded to C = 0.025~0.15% and E = 10~30 kV (Okuzaki et al., 2008). Here, a rise
the ambient humidity from 50 to 70 %RH increased in the electric current at E = 20 kV from
1.7 to 2.6 µA and brought about rapid growth of the yarn. On the other hand, the current
was less dependent on the humidity in the absence of the PXTC in the solution (0.39-0.46 µA
at E = 20 kV). This clearly indicates that the ionic conduction of the PXTC crucially
Uniaxially Aligned Poly(p-phenylene vinylene)
and Carbon Nanofiber Yarns through Electrospinning of a Precursor

143
influences the yarn formation. Indeed, the similar phenomenon was observed for other ionic
conducting polyelectrolyte such as poly(acrylic cid). Fig. 4 shows influence of PXTC
concentration on average diameter of the yarn, spinning rate, and viscosity of the solution.
At E = 20 kV, the yarn was formed at C = 0.025%-0.15%, while at C > 0.15%, no yarn was
formed at E up to 30 kV since the viscosity of the solution (> 8.8 cP) was too high to
maintain a continuous jet from the spinneret. On the other hand, at C < 0.025%, small
droplets of the solution were collected on the surface of the aluminum target due to the low
viscosity (< 1.2 cP) and surface tension not enough to maintain a stable drop at the spinneret.
Thus, methanol crucially increases the volatility of solvent as well as decreases the surface
tension, which arises from the fact that dilution with pure water never yields yarn.

Fig. 4. Dependence of PXTC concentration on average diameter of the yarn and spinning
rate at E = 20 kV in 10 min and viscosity of the solution measured at 30 °C with a
viscometer. Dependence of applied voltage on average diameter of the yarn at C = 0.1 % in
10 min was also plotted (broken line).
The average diameter of the yarn electrospun at E = 20 kV in 10 min increased from 5 to 100
µm with decreasing of C from 0.15% to 0.025%. This can be explained by the increase of
spinning rate, defined as the average volume of the solution electrospun in 1 min, due to the
decrease of viscosity. A further decrease of viscosity, however, yields finer yarns due to the
decrease of C. The effect of applied voltage on average diameter of the yarn was also
demonstrated in Fig. 4 (broken line), where the electrospinning was carried out at a constant
Ferroelectrics

144
C of 0.1% for 10 min. It is found that the average diameter of the yarn is less dependent on
the applied voltage and the value is about 100 µm, where the yarns were as long as the gap
between the spinneret and the target electrode (20 cm). A further electrospinning resulted in
a deposition of the droplets on the yarns before the solvent evaporated completely, which
allowed the yarns to fall down on the target electrode due to their own weight.
3.2 Uniaxially aligned PPV nanofiber yarns by thermal conversion of PXTC
TG curve of the PXTC yarns (solid line) is divided into three major steps in terms of weight
loss, as shown in Fig. 5: The first small weight loss at 25-100 °C is associated with the
desorption of moisture, and the second one at 100-250 °C is due to the elimination of
tetrahydrothiophene and hydrochloric acid, corresponding to the conversion to PPV (as
shown in the inset) (Okuzaki et al., 1999). The third weight loss at 500-600 °C continuing
gradually up to 1000 °C is due to the carbonation of the PPV that will be discussed later
(Ohnishi et al., 1986). The PXTC yarns are subsequently converted to PPV yarns by heat
treatment at 250 °C for 12 h in vacuum (Okuzaki et al., 1999). About 42% weight loss of the
as-electrospun PXTC yarns in a temperature range of 25-300 °C, decreases to less than 0.01%
after the thermal conversion, demonstrating that the precursor unit is completely converted
to PPV.
Fig. 6 shows FT-IR spectra of PXTC yarns electrospun at C = 0.1% and E = 20 kV and PPV
yarns converted at 250 °C for 12 h in vacuum. The FT-IR spectrum of the resulting PPV
yarns shows a clear peak at 965 cm
-1
assigned to the trans-vinylene C–H out-of-plane bend,
while an absorption peak at 632 cm
-1
to the C–S stretch of the PXTC disappeared completely.
A clear indication of paracrystalline structure is seen in a wide-angle X-ray diffraction
pattern as shown in Fig. 7. The PPV yarns show clear peaks at 2θ = 20.5° (d = 4.33 Å) and

146
28.2° (d = 3.16 Å), and a shoulder at 2θ = 22.0° (d = 4.03 Å), corresponding to the diffractions
from (110), (210), and (200) planes of the monoclinic unit cell of the PPV crystal, respectively
(Masse et al., 1989). Since the as-spun PXTC fibers are amorphous, the crystallization will
take place during the thermal conversion to PPV. The degree of crystallinity estimated from
the WAXD pattern is ca. 45 % and the apparent crystallite size normal to the (210) plane
calculated from Scherrer’s equation is 75 Å. The diffraction patterns of the side and end
views of the PPV yarns are substantially the same, indicating no notable orientation of PPV
chains on a molecular level.

Fig. 8. SEM micrographs of PPV yarn fabricated by thermal conversion of the PXTC yarn
elecctrospun at C = 0.1% and E = 20 kV for 10 min.
It is seen from Fig. 8, a μm-thick yarn is composed of numerous PPV nanofibers uniaxially
aligned along the axis of the yarn. It is noted that the PPV fibers preserve their morphology
even after the elimination reaction. An influence of PXTC concentration on distribution of
diameters for the PPV nanofibers is demonstrated in Fig. 9. At C = 0.05~0.15%, a distribution
peak of the fiber diameter locates between 100-200 nm, where more than 50% of fibers have
a diamter less than 200 nm. Particularly, at C = 0.1%, more than 25% of fibers are finer than
100 nm. In contrast, more than 30% of fibers are thicker than 500 nm with a wide
distribution at C = 0.025%, which is ascribed to the association or fusion of fibers since the
solvents may not evaporate completely due to the low concentration. Furthermore, effects of
electric field on distribution of fiber diameter and orientation of the PPV nanofibers were
demonstrated in Fig. 10. Although the distribution of fiber diameter is less dependent on the
electric field, orientation of the PPV nanofibers along the axis of the yarn is improved as the
voltage becomes higher, in which the ratio of fibers having a tilt angle smaller than 10°
increases from 44% (E = 10 kV) to 60% (E = 30 kV). This can be explained by the electrostatic
repulsion between positively charged fibers deposited on the yarn (Li et al., 2004) and/or
explained by stretching the fibers due to the electrostatic force between the spinneret and
the yarn in favor of discharging through the yarn, leading to a configuration in parallel
alignment (Okuzaki et al., 2008).
3.3 Conducting PPV nanofiber yarns by acid doping
The doping is performed by dipping the PPV nanofiber yarns in conc. H
2
SO
4
at room
temperature. After doping, the nanofiber yarns were soaked in a large amount of
acetonitrile and dried under vacuum. Fig. 11 shows current-voltage relationship for PPV
Uniaxially Aligned Poly(p-phenylene vinylene)
and Carbon Nanofiber Yarns through Electrospinning of a Precursor

Fig. 10. Dependence of applied voltage on distribution of fiber diameter and orientation of
PPV nanofibers along the axis of the yarn (C = 0.1%).
Ferroelectrics

148
and H
2
SO
4
-doped PPV nanofiber yarns measured with a digital multimeter (model 2000,
Keithley) by a two-probe method where the nanofiber yarns were placed on two gold
electrodes kept at an interval of 2 mm. No detectable current was observed in a voltage
range of -5~+5 V for the PPV nanofiber yarns, demonstrating that the PPV has extremely
low conductivity in the neutral state due to the small carrier density. Upon doping with
H
2
SO
4
, the color changed from yellowish brown to black and apparent current flowed
through the nanofiber yarns, where the current almost linearly increased in this voltage
range and the value attained 1~2 μA at 5 V (Okuzaki et al., 2008). Although the conductivity
of a single nanofiber can not be estimated because mean value of the cross-sectional area in
the nanofiber yarns is unknown, the results clearly indicate that the electrical conductivity of
the PPV nanofiber yarns increases by doping with H
2
SO
4
.

Fig. 12. Schematic illustration of proposed doping mechanism of PPV.
This can be explained by oxidation of PPV to produce charge carriers where anions are
intercalated between polymer chains as counter ions (Okuzaki et al., 2005). However, the
doping of PPV with protonic acids has not been fully understood yet (Ahlskog et al., 1997).
Han et al. have found that non-oxidizing protonic acids can be effective dopants for a wide
Uniaxially Aligned Poly(p-phenylene vinylene)
and Carbon Nanofiber Yarns through Electrospinning of a Precursor

149
range of conjugated polymers (Han & Elsenbaumer, 1989). The mechanism of protonic acid
doping appears to involve direct protonation of the polymer backbone followed by an
internal redox process that gives polarons as the predominant charge defects, similarly to
polyaniline (Chiang & MacDiarmid, 1986).
3.4 Uniaxially aligned carbon nanofibers by thermal conversion of PXTC
It is seen from the TG curve as shown in Fig. 5, the third weight loss at 500-600 °C
continuing gradually up to 1000 °C is due to the carbonization of the PPV (Ohnshi et al.,
1986). As a comparison, the TG curve of PAN, a typical precursor of carbon fiber (broken
line), shows a significant weight loss of about 40% between 300 and 500 °C. This
corresponds to the carbonation, involving dehydrogenation, cyclization, and polymerization
of nitrile groups, and then losing noncarbon elements, such as HCN, NH, and H, in the form
of volatile gases. As a result, the carbon yield for the PXTC was 25% at 1000 °C, which was
somewhat smaller than that for the PAN (30%).

Fig. 13. SEM micrographs and distribution of fiber diameter for various nanofiber yarns
thermally treated at various temperatures.
Fig. 13 shows SEM micrographs and distribution of fiber diameter for the PXTC yarns
thermally treated at various temperatures. Although we failed to measure SEM micrographs
of the as-electrospun PXTC yarns owing to the elimination of tetrahydrothiophene and
hydrochloric acid under the radiation of an electron beam, it can be considered that the fiber
diameter decreases during the thermal conversion to PPV based on the fact that nearly 50%
of weight is lost up to 250 °C (Fig. 5). Agend et al. (2007) fabricated carbon nanofibers by
electrospinning of PAN from DMF solution and subsequent carbonization and found that
average diameter of PAN nanofibers decreased from 149 to 109 nm by carbonization at 1100
°C. It should be emphasized in Fig. 13 that the fibers preserve their morphology with
average diameters d = 133-184 nm. Interestingly, the nanofibers were uniaxially aligned
along the axis of the yarn, similarly as observed in PPV nanofibers where about 70% of
Ferroelectrics

150
nanofibers in the yarn had a tilt angle less than 30° (Okuzaki et al., 2008). Furthermore, there
was no notable change in the morphological structure and the distribution of fiber diameter
even at temperatures higher than 500-600 °C of the third weight loss where the
carbonization of the PPV occurs.
Raman spectroscopy is one of the most sensitive tools for providing information on the
crystalline structure of carbon fibers. The highly ordered carbon such as a single hexagonal
crystal graphite shows a strong peak at 1582 cm
-1
(G band) from in-plane modes with E
2g

symmetry, while the disordered carbon due to imperfection or lack of hexagonal symmetry
shows a broad peak at 1360 cm
-1
(D band) (Kim et al., 2004). A clear evidence of the
structural change caused by the carbonization is demonstrated in Fig. 14. Two peaks at
around 1580 and 1360 cm
-1
, assigned to G and D bands, respectively, evidently appear in the
Raman spectra for the nanofiber yarns thermally treated at temperatures higher than 600 °C,
indicating practical transformation of disordered carbon into graphitic structure in the
carbonization process. It notes that the carbonization took place without melting process
accompanying the third weight loss at 500-600 °C, suggesting that the PPV is
intermolecularly condensed to form more compact structures by removal of hydrogen and
aromatization (Ohnishi et al., 1986) as shown in Fig. 15, similarly to carbonization of poly(p-
phenylene) (Fitzer et al., 1971).

Lespade et al. (1984) identified four graphitization indices: (i) the wavenumber of the G
band, (ii) the band width of the G band, (iii) the intensity ratio of the D and G bands, and
(iv) the band width of the second order phonon. Especially, the intensity ratio of the D and
G bands is one of the most important parameters characterizing not only the degree of
graphitization but also defects in the carbonaceous materials. Using a mixed Gaussian-
Lorentzian curve-fitting procedure, the ratio of the integrated intensity (R) of the D (I
D
) and
G bands (I
G
) is calculated as

Fig. 14. Raman spectra of various nanofiber yarns thermally treated at various temperatures.
Uniaxially Aligned Poly(p-phenylene vinylene)
and Carbon Nanofiber Yarns through Electrospinning of a Precursor

151

Fig. 15. Schematic illustration of pyrolysis of PPV.

Fig. 16. Dependence of carbonization temperature on R and L
a
values for various carbon
nanofiber yarns.
R = I
D
/ I
G
(1)
The R is also sensitive to the concentration of graphite edge planes and/or crystal
boundaries relative to standard graphite planes. Knight and White (1989) investigated the
relation between R and the graphitic crystallite size (L
a
) for Tuinstra and Koenig’s original
data plus such additional data from the literature (Tuinstra & Koenig, 1970). They found the
inverse relation between R and L
a
and developed an empirical formula as
L
a
= 4.4 / R (2)
In Fig. 16, the values of R and L
a
for the nanofibers carbonized at 600-1000 °C are 3.1-3.7 and
1.2-1.4 nm, respectively, which are similar to those of the PAN-derived carbon nanofibers
(Wang et al., 2003). Since the Raman spectra do not change at the carbonization
temperatures between 600 and 1000 °C, the variation of the R value is considered to be
Ferroelectrics

152
within the experimental error. Assuming that the I
G
and I
D
are proportional to the number
of the scattering ordered and disordered sp
2
bonding carbon atoms, their molar fractions X
G

and X
D
can be defined as follows.
X
G
= I
G
/ (I
G
+ I
D
) = 1 / (1 + R) (3)
X
D
= I
D
/ (I
G
+ I
D
) = R / (1 + R) (4)
From equations (2)-(4), the higher the degree of graphitization, the higher the X
G
and L
a
, but
the lower the X
D
and R. The values of X
G
and X
D
were calculated as 0.21-0.24 and 0.76-0.79
for the resulting carbon nanofiber yarns, respectively.
4. Conclusion
Unlike conventional electrospun polymer fibers deposited on a target electrode as a
randomly oriented mesh, PXTC was electrospun into centimeters-long yarns vertically on
the surface of the electrode but parallel to the electric field. The formation of the yarn was
strongly influenced by the concentration, applied voltage, and relative humidity. The
subsequent thermal conversion of thus-electrospun PXTC yarns was carried out at 250 °C
for 12 h in vacuum and resulted in the uniaxially aligned PPV nanofibers with an average
diameter of 150 nm. The applied voltage enhanced orientation of PPV nanofibers along the
axis of the yarn, while the distribution of fiber diameter was less dependent on the applied
voltage. WAXD analysis indicated that the PPV nanofibers exhibited paracrystalline
structure with crystallinity and crystallite size of 45% and 75 Å, respectively. Furthermore,
doping with sulfuric acid changed the color from yellowish brown to black and brought
about a significant increase in the electrical conductivity of the PPV nanofiber yarn. The
uniaxially aligned carbon nanofibers with average diameters of 133-184 nm were
successfully fabricated by carbonization of the PXTC nanofiber yarns. The graphitic
crystallite size and the molar fraction of the ordered sp
2
bonding carbon atoms in the
resulting carbon nanofiber yarns carbonized at 60-1000 °C were 1.2-1.4 nm and 0.21-0.24,
respectively. Thus, we succeeded in fabricating uniaxially aligned semiconducting,
conducting, and carbon nanofiber yarns by electrospinning and subsequent thermal
conversion or carbonization of PXTC, which would open up a new field of applications in
organic nanoelectronics such as elecctromagnetic interference shielding, conducting textiles,
and high-sensitive sensors and fast-responsive actuators utilizing their high speccific surface
area.
5. References
Agend, F.; Naderi, N. & Alamdari, R. F. (2007). Fabrication and electrical characterization of
electrospun polyacrylonitrile-derived carbon nanofibers, J. Appl. Polym. Sci., 106,
255-259.
Ahlskog, M.; Reghu, M.; Noguchi, T. & Ohnishi, T. (1997). Doping and conductivity studies
on poly(p-phenylene vinylene), Synth. Met., 89, 11-15.
Burrourghes, J. H.; Bradley, D. D. C.; Brown, A. R.; Marks, R. N.; Mackay, K.; Friend, R. H.;
Burns, P. L. & Holmes, B. (1991). Light-emitting diodes based on conjugated
polymers, Nature, 347, 539-541.
Uniaxially Aligned Poly(p-phenylene vinylene)
and Carbon Nanofiber Yarns through Electrospinning of a Precursor

Fig. 1. The unique spontaneous polarization of ferroelectric materials
Carbon materials are used extensively in various forms in a variety of systems, because of
their high thermal and chemical stability, and excellent mechanical, electrical, and elec-
trochemical properties, which can be maximized by using an appropriate process. The
various useful properties of carbon materials are attributed to their unique structures as
shown in Fig.2 (Wei et al., 1993; Cousins, 2003; Frondel & Marvin, 1967; Kroto et al., 1985;
Wang et al., 2009). Diamonds are famous for their impressive mechanical properties, which
result from the strong covalent bonds based on sp
3
hybridization only between carbon
atoms. On the other hand, carbon materials, such as fullerenes and carbon nanotubes
Ferroelectrics

156
(CNTs), have excellent electrical or electrochemical properties, such as low resistance, due to
the π-π conjugations based on sp
2
hybridization. Of the abovementioned carbon materials
sp
2
carbon materials are attractive for use with ferroelectric and related materials, due to
their excellent electrical properties, such as good conductivity and low resistance.
Therefore, this chapter introduces carbon materials, with their unique and excellent
properties, for applications in ferroelectric and related materials.

Fig. 2. Carbon materials in various multi-atomic structures with different chemical
configurations: (a) diamond, (b) graphite, (c) lonsdaleite, (d) C60, (e) C540, (f) C70, (g)
amorphous carbon, and (h) single-walled carbon nanotube
2. Ferroelectric materials assisted by carbon materials
Ferroelectric random access memory (FeRAM) has been considered for non-volatile
memories, because it has the lowest power consumption among various semiconductor
memories and its operation speed is similar to that of dynamic RAM (DRAM) (Arimoto &
Ishiwara, 2004). A single ferroelectric-gate FET (field effect transistor) is the main
component of FeRAM. However, fabricating ferroelectric-gate FETs with excellent electrical
properties is difficult, due to the diffusion problem. When a ferroelectric material, such as
lead zirconate titanate (PZT), is deposited directly on a Si substrate, forming a film, the
constituent element of the substrate and film are diffused, or mixed, during the
crystallization process. One way to avoid this diffusion problem is to insert an insulating
buffer layer between the Si substrate and a ferroelectric film. Fig.3. shows the resulting gate
structure, either an MFIS (Fig.3(a)) or MFMIS (Fig.3(b)) structure (M: metal, F: ferroelectrics,
I: insulator, and S: semiconductor) (Ishiwara, 2009). However, inserting the buffer layer
raises new problems, such as short data retention time and high operation voltage. Using
CNT is one of the efficient methods for solving these problems.
Applications of Carbon Materials for Ferroelectric and Related Materials

157

Fig. 3. Schematic drawings of (a) MFIS and (b) MFMIS gate structures (Ishiwara, 2009)
Whereas an insulating buffer layer is usually inserted between a Si substrate and the
ferroelectric film in a ferroelectric-gate Si transistor, direct contact between the substrate and
the ferroelectric film (MFS structure) can be achieved in a ferroelectric-gate CNT transistor
(Fig.4.), due to the absence of dangling bonds on the surface of ideal CNTs. The direct
contact in a ferroelectric-gate FET is expected to achieve longer data retention time with a
lower operation voltage than that in a FET with MFIS gate structure, because no
depolarization field is generated in the ferroelectric film. In addition, the high current
drivability of CNTs also enables ferroelectric-gate CNT transistors to be one of the most
promising candidates for future high-density non-volatile memories.
The current through a CNT in CNT transistors comes from thermally assisted tunneling
through the source Schottky barrier J. Appenzeller, M. Radosavljevic, J. Knoch and Ph.
Avouris, Phys. Rev. Lett. 92 (2004), p. 048301. (Appenzeller et al., 2004). Thus, the gate
voltage lowers the Schottky barrier height and produces a high electric field at the
semiconductor surface, rather than modulating the channel conductance. In addition, in the
MFS structure, no depolarization field is expected to be generated in the ferroelectric film
with zero external voltage. Thus, zero electric field exists for both directions of the remnant
polarization. As a result, the polarization direction in the ferroelectric film is hard to be read
out by drain current in a FET with drain electrodes and a Schottky barrier source. Therefore,
it is easier to discuss the operation characteristics of ferroelectric-gate CNT transistors, semi-
quantitatively.
A simplified current modulation model at the source Schottky barrier in a Si transistor can
be applied to a ferroelectric-gate CNT after changing the dielectric gate insulator to a
ferroelectric (Tsutsui & Asada, 2002). Fig.5 is a one-dimensional energy band diagram at the
source edge in a ferroelectric-gate FET and it assumes that the work functions of the gate
and source metals are the same. Because a CNT transistor has a very thin semiconductor
thickness as shown in Fig.5, the semiconductor can be assumed to be an insulator, when the
doping density of the CNT is not very high. This assumption enables the source region in
the ferroelectric-gate FET to be expressed as an MFIM structure, which is indicated in the
dotted square of Fig.4. In an MFIM structure, the first M is the gate metal, F is a ferroelectric,
I is a CNT, and the last M is the source metal. A graphical method can be used in this one-
dimensional structure to calculate electric fields in both F and I films easily (Ishiwara, 2001).
Interestingly, the depolarization field appears even in a CNT transistor with MFS gate
structure.
The average electric field in the semiconductor can be calculated under the assumption that
relative dielectric constant of the semiconductor is the same as that of Si (11.8) and the
ferroelectric film has the remnant polarization of 3 μC/cm
2
and a square-shaped P-V
hysteresis. Moreover, the calculated average electric field in the semiconductor is 3 MV/cm,
Ferroelectrics

158
which is independent of the semiconductor thickness. Because the calculated value is much
higher than the dielectric breakdown field of Si, which is less than 1MV/cm, sufficient
charge can be injected into the semiconductor when the electric field lowers the Schottky
barrier height. However, the depolarization field in the ferroelectric film is not high, which
can be explained by the diagram as shown in Fig.5. The product of film thickness and
electric field, which is the voltage across the film, was the same between the ferroelectric
and semiconductor films under the zero bias condition. Moreover, holes were injected after
the application of negative gate voltage, whereas no holes were injected after the application
of a positive gate voltage. Combining this charge injection model with the voltage drop
model at the drain Schottky barrier (Tsutsui, 2002) produced I
D
–V
D
characteristics of a
ferroelectric-gate CNT FET.
Ishiwara reported two structures, CNTs deposited with SiO
2
/Si and SBT/Pt/Ti/SiO
2
/Si
structures using a spin-coated method. In the CNTs deposited with SiO
2
/Si structure, Si
substrate is used as the gate electrode in the MOS-CNT transistors, whereas a Pt film is used
in the CNTs deposited with SBT/Pt/Ti/SiO
2
/Si ferroelectric-gate FETs. However, both
transistors had charge injection-type hysteresis loops. Therefore, the first step for realizing
ferroelectric-gate CNT transistors is elimination of the spurious hysteresis loops.

Fig. 5. One-dimensional energy band diagram at the source edge in a ferroelectric-gate
Schottky FET (Ishiwara, 2009)
3. Piezoelectric materials assisted by carbon composites
Cement-based piezoelectric composites have been studied for applications, such as sensors
and actuators in civil engineering (Li et al., 2002; Cheng et al., 2004; Chaipanich et al., 2007).
These sensors and actuators have a great potential to be used for non-destructive
performance monitoring of bridges and dams, for example (Sun et al., 2000). The
Applications of Carbon Materials for Ferroelectric and Related Materials

159
piezoelectric composites have been prepared with a variety of different connectivity
patterns, and the 0-3 connectivity is the simplest (Newnham et al., 1978). In a 0-3 cement-
based piezoelectric composite, a three-dimensionally connected cement was loaded with a
zero-dimensionally connected active piezoelectric ceramic particles. PZT is mainly used for
piezoelectric ceramic and has high dielectric constant and density, which results good
piezoelectric properties. The 0-3 cement-based piezoelectric composite is also compatible
with concrete, the most popular host material in civil engineering. In addition, cement-based
composites are easy to manufacture and amenable to mass production (Li et al., 2002;
Huang et al., 2004; Cheng et al., 2005). However, the 0-3 cement-based piezoelectric
composites are complicated by poling because the ceramic structure does not form a
continuously connected structure across the inter-electrode-dimension. The difficulty of
poling is mainly due to the high electric impedance and piezoelectric activities of the
composites are lower than those of pure ceramics. Thus, the poling field and the poling
temperature should be increased to facilitate poling of the ceramic particles in the
composites. However, if the poling voltage is too high, the samples can be broken down or if
a poling temperature is too high, the mechanical properties of the cement can be weaken.
Therefore, improving the electrical conductivity of the cement matrix is one of the efficient
methods to increase the polarization of the composite.
Carbon materials have excellent electrical properties and are often used to enhance the
conductivity of other composites. Shifeng et al. investigated the effect of carbon black on the
properties of 0-3 piezoelectric ceramic/cement composites (Shifeng et al., 2009). The
composites were manufactured using sulphoaluminate cement and piezoelectric ceramic
[0.08Pb(Li
1/4
Nb
3/4
)O
3
·0.47PbTiO
3
·0.45PbZrO
3
][P(LN)ZT] as raw materials with a
compression technique. The piezoelectric strain constant d
33
of the composites with carbon
black content was as shown in Fig.9. The piezoelectric strain constant at its maximum was
42% larger than that of the composite without carbon black when 0.3 wt% content of the
carbon black was used, and decreased when the content of carbon black was beyond 0.3
wt%. The Maxwell-Wagner model can explain this trend. The following equation (1) gives
the ratio of the electric field acting on the ceramic particles and matrix phases in a 0-3
piezoelectric composite with the conductivity (Blythe, 1979).
E
1
/E
2
= σ
2
/σ
1
(1)
where σ
1
and σ
2
are the electric conductivity of the ceramic and the matrix, respectively. It is
noteworthy that the electric field working on the ceramic particles is controlled by the ratio
(σ
2
/σ
1
). Because the conductivity of ceramic particles is much higher than that of the cement
matrix, σ
2
/σ
1
is small. Thus, the addition of a small amount of a conductive material, such as
carbon materials, decreases the impedance of the composite and increases the electric
conductivity of the composite. As a results, the electric conductivity of the cement matrix
increases, resulting in easier poling. Therefore, up to a suitable amount of carbon black
addition, the piezoelectric constant d
33
increases gradually, whereas with more than 0.3 wt%
of the amount of carbon black added, the piezoelectric properties is decreased, because the
higher voltage could not be established during the poling process. Gong et al. also reported
the piezoelectric and dielectric behavior of 0-3 cement-based composites mixed with carbon
black (Gong et al., 2009). They fabricated 0-3 cement-based composites from white cement,
PZT powder and a small amount of carbon black and found similar results to those of a
poling process of the composite at room temperature that was facilitated by the addition of
Ferroelectrics

160
carbon black; the piezoelectric properties of the composite were improved. It was also found
that when too much carbon black was added, the piezoelectric properties of the composite
decreased, due to the conductive properties of the carbon black. Sun et al. also found that
carbon fiber could be used for piezoelectric concrete (Sun et al., 2000).

Fig. 6. Variation of piezoelectric strain constant d
33
of the composites with carbon black
content (Shifeng et al., 2009)
As for the piezoelectric cement composites, the piezoelectric properties of the polymer
composites can be facilitated by addition of the conductive carbon materials. Sakamoto et al.
reported acoustic emission (AE) detection of PZT/castor oil-based polyurethane (PU) with
and without graphite doping (Sakamoto et al., 2002). The piezoelectric and pyroelectric
properties of the composite increased with graphite doping, due to the enhanced
conductivity/reduced resistance caused by graphite doping. Moreover, the piezoelectric
coefficient d
33
varied with the carbon content with similar behavior to that of the
piezoelectric cement composites, as shown in Fig.7. As a result, two simulated sources of
AE, ball bearing drop and pencil lead break, were detected better with the graphite doped
PZT/PU composite. This can be also explained by the aforementioned Maxwell-Wagner
interfacial mechanism.
Piezoelectric polymer composites can be also useful as mechanical damping composites
(Hori et al., 2001). PZT/carbon black/epoxy resin composites were manufactured and their
mechanical and damping properties were investigated. A measure of mechanical of
damping intensity, the mechanical loss factor (η), reached its maximum at a certain level of
carbon black added and decreased above that as shown in Fig.8. In this composite, carbon
black had an additional function: when the mechanical energy from vibrations and noises
was transformed into electrical energy (current) by PZT, the electric current was conducted
to an external circuit through CB powders and then dissipated as thermal energy through a
resistor.
Applications of Carbon Materials for Ferroelectric and Related Materials

161

Fig. 7. Variation of the piezoelectric coefficient d
33
with the carbon contents in the composite
film (Sakamoto et al., 2002)

Fig. 8. Variation of piezoelectric strain constant d
33
of the composites with carbon black
content (Hori et al., 2001)
Unlike the studies described so far, Li et al. reported that piezoelectric material improve the
properties of carbon materials (Li et al., 2010). The single crystal PMN-PT (lead magnesium
niobate-lead titanate, which has a chemical formular of (1-x)[Pb(Mg
1/3
Nb
2/3
)O
3
] and
x[PbTiO
3
], was embedded in the two different activated carbons (NAC and HAC), and
hydrogen adsorption of the composite was investigated. Hydrogen adsorption of the
composite was enhanced due to an electric field generated from the piezoelectric material,
and the amount of the enhancement was proportional to the charges generated by the
piezoelectric materials. Therefore, higher hydrogen adsorption was achieved because higher
pressure creasted more charges (Fig.9 and 10). Hydrogen adsorption at lower temperatures
Ferroelectrics

162
was much greater than that at higher temperatures, because the electric field has a great
effect on the bonding of hydrogen molecules more when the kinetic energy of the molecules
is lower at lower temperatures (Fig.10).

Fig. 10. PMN–PT effect on H
2
adsorption of NAC and HAC at 77 K under various pressures
(Li et al., 2010)
5. Conclusion
In this chapter, carbon materials were introduced to assist the application of ferroelectric
related materials. Ferroelectric-gate CNT transistors use the unique interfacial and electrical
properties of CNTs to a longer data retention time of the transistor. In all of the piezoelectric
Applications of Carbon Materials for Ferroelectric and Related Materials

2
Brazil
1. Introduction
The dielectric relaxation phenomenon in ferroelectric materials reflects the delay (time
dependence) in the frequency response of a group of dipoles when submitted to an external
applied field. When an alternating voltage is applied to a sample, the dipoles responsible for
the polarization are no longer able to follow the oscillations of the electric field at certain
frequencies. The field reversal and the dipole reorientation become out-of-phase giving rise
to a dissipation of energy. Over a wide frequency range, different types of polarization
cause several dispersion regions (Figure 1) and the critical frequency, characteristic of each
contributing mechanism, depends on the nature of the dipoles. The dissipation of energy,
which is directly related to the dielectric losses, can be characterized by several factors: i- the
losses associated to resonant processes, characteristics of the elastic displacing of ions and
electrons, and ii- the dipolar losses, due to the reorientation of the dipolar moment or the
displacing of the ions between two equilibrium positions.
For ferroelectric materials the dielectric relaxation mechanisms are very sensitive to factors
such as temperature, electric field, ionic substitution, structural defects, etc. The defects
depend on either intrinsic or extrinsic heterogeneities due to special heat treatments, ionic
substitutions, grain size additives, and grain boundary nature. On the other hand, structural
defects may cause modifications of the short and/or long-range interactions in ferroelectric
materials. From this point of view, apart from the localized dipolar species, free charge
carriers can exist in the material. Several physical processes cause the decay of the electrical
polarization: dipolar reorientation, motion of the real charges stored in the material and its
ohmic conductivity. The former is induced by thermal excitations, which lead to decay of
the resultant dipolar polarization. The second process is related to the drift of the charges
stored in the internal field of the sample and their thermal diffusion. With the increase of the
temperature, the dipoles tend to gradually disorder owing to the increasing thermal motion
and the space charges trapped at different depths are gradually set free. Thus, the electrical
conductivity in ferroelectric materials affects the physical properties because of there will be
a competition between the ferroelectric phase and free charge carriers.
Ferroelectrics

166

Fig. 1. General representation of relaxation and resonance types
The oxygen vacancies are always related to dielectric relaxation phenomenon, as well as to
the electrical conductivity for ferroelectric perovskite-related structures, considering that
these are the most common mobiles species in such structures (Jiménez & Vicente, 1998;
Bharadwaja & Krupanidhi, 1999; Chen et al., 2000; Islam, 2000; Yoo et al., 2002; Smyth, 2003;
Verdier et al., 2005). For ABO
3
-type perovskite structures, the BO
6
octahedra play a critical
role in the demonstration of the ferroelectric properties. It has been reported that the
ferroelectricity could be originated from the coupling of the BO
6
octahedra with the long-
range translational invariance via the A-site cations (Xu, 1991). In this way, the breaking of
the long-range translational invariance results in the dielectric relaxation phenomenon. The
degree of the coupling between neighboring BO
6
octahedra will be significantly weakened
by introducing defects, such as vacancies. On the other hand, for the layered ferroelectric
perovskites (Aurivillius family, [Bi
2
O
2
]
2+
[A
n−1
B
n
O
3n+1
]
2−
), the oxygen vacancies prefer to stay
in the Bi
2
O
2
layers, where their effect upon the polarization is considered to be small, instead
of the octahedral site, which controls the polarization. The origin of the dielectric behavior
for these materials have been associated to a positional disorder of cations on A- or B-sites of
the perovskite layers that delay the evolution of long-range polar ordering (Blake et al.,
1997; Ismunandar & Kennedy, 1999; Kholkin et al., 2001; Haluska & Misture, 2004; Huang et
al., 2006).
For at least several decades, the dielectric response of ferroelectric materials (polycrystals,
single crystals, liquids, polymers and composites) has been of much interest to both
experimentalists and theorists. One of the most attractive aspects in the dielectric response
of ferroelectric materials is the dielectric relaxation phenomenon, which can show the direct
connection that often exists between the dipolar species and the charge carriers in the
materials. Researchers typically fit the complex dielectric permittivity data according to a
relaxation theoretical model, which is representative of the physical processes taking place
in the system under investigation.
The complex dielectric permittivity (ε) can be expressed as:
( ) ( ) ( ) i ε ω ε ω ε ω ′ ′′ = − (1)
Dielectric Relaxation Phenomenon in Ferroelectric Perovskite-related Structures

167
where ω is the angular frequency; ε' is the real component, which is in phase with the
applied field; ε'' is the imaginary component, which is in quadrature with the applied field.
Both components of the complex dielectric permittivity are related each other by the
Kramers-Kronig relations.
The Debye’s model (Debye, 1929), which considers not-interacting dipoles, proposes the
following expression for the complex dielectric permittivity:
( )
1
s
i
ε ε
ε ω ε
ωτ
∞
∞
−
= +
+
(2)
where τ is the relaxation time, ε
s
is the statical dielectric permittivity (at very low
frequencies) and ε
∞
, the dielectric permittivity at high frequencies.

168
where z=ln(τ), Δε’=ε
s
-ε
∞
, and β=(1-α), where α shows the deformation of the semicircle arc
in the Cole-Cole plot, i.e. it is the angle from the ε’ axis to the center of the semicircle arc.
The temperature dependence for the relaxation time follows the Arrhenius dependence
given as:
exp
o
B
Ea
k T
τ τ
⎛ ⎞
=
⎜ ⎟
⎝ ⎠
(6)
where E
a
is the activation energy of the relaxation process, k
B
is the Boltzmann’s constant, T
is the temperature and τ
o
is the pre-exponential factor. By using this dependence, the
activation energy value of the dielectric relaxation process can be calculated and the
mechanism, or mechanisms, associated to it be evaluated.
On the other hand, it has been previously commented that for ferroelectric materials (for
dielectrics in general) the charge carriers have to be taking into account in the dielectric
relaxation mechanisms. When an electric field is applied to the material, there is the known
reorientation of the dipoles but also the displacement of the charge carriers. Therefore, the
electrical conductivity behavior should be considered.
In order to evaluate the frequency dependent conductivity, the Universal Relaxation Law
(Jonscher, 1996) can be used, where the electrical conductivity can be expressed as:
( ) 1
n
dc
H
A
ω
σ ω σ ω
ω
⎡ ⎤
⎛ ⎞
⎢ ⎥ = + +
⎜ ⎟
⎢ ⎥
⎝ ⎠
⎣ ⎦
(7)
where σ
dc
, ω
H
, n and A are the dc conductivity, the onset frequency of the ac conductivity
(mean frequency of the hopping process), the exponent and the weakly temperature
dependent term, respectively. The first and the second terms of the equation (7) refer to the
universal dielectric response (UDR) and to the nearly constant loss (NCL), respectively.
The power-law frequency dependent term (UDR) originates from the hopping of the carriers
with interactions of the inherent defects in the materials, while the origin of the NCL term
(the linear frequency dependent term) has been associated to rocking motions in an
asymmetric double well potential (Nowick & Lim, 2001). For NCL term, the electrical losses
occur during the time regime while the ions are confined to the potential energy minimum
(León et al., 2001).
Both the dc conductivity and the hopping frequency are found to be thermally activated
following an Arrhenius dependence (equations 8 and 9), being U
dc
and U
H
the activation
energies of the dc conductivity and the hopping frequencies of the carriers, respectively, and
σ
o
and ω
o
the pre-exponential factors. It has been interpreted by using different theoretical
models (Funke, 1993; Ngai, 1993; Jonscher, 1996) as indicating that the ac conductivity
originates from a migration of ions by hopping between neighboring potential wells, which
eventually gives rise to dc conductivity at the lowest frequencies.
exp
dc
dc o
B
U
T
k T
σ σ
⎛ ⎞
= −
⎜ ⎟
⎝ ⎠
(8)
exp
H
H o
B
U
k T
ω ω
⎛ ⎞
= −
⎜ ⎟
⎝ ⎠
(9)
Dielectric Relaxation Phenomenon in Ferroelectric Perovskite-related Structures

169
The objective of the present chapter is conducted to discuss the dielectric relaxation
phenomenon in ferroelectric perovskite-related structures considering the relaxation
mechanisms and the influence of the vacancies on them, so that the results can be more
easily understood, from the physical point of view. Examples are given from the previously
reported work of the present authors, as well as from the literature, with preference to the
formers.
2. Ferroelectric ABO
3
perovskites.
Perovskite type oxides of general formula ABO
3
are very important in material, physics
and earth sciences because they exhibit excellent physical properties, which make them
especial candidates for a wide application range in the electro-electronic industry (Lines,
1977). They are known for their phase transitions, which may strongly affect their physical
and chemical properties. Perovskite structure-type oxides exist with all combination of
cation oxidation states, with the peculiar characteristics that for ABO
3
compounds one of
the cations, traditionally the A-site ion, is substantially larger than the other one (B-site).
This structure seem to be a particularly favorable configuration, because it is found for an
extremely wide range of materials, where its basic pattern is frequently found in
compounds that differ significantly from the ideal composition. From a direct review of
the current literature, it has been established as well that important defects in the
perovskite structure are directly related to vacancies of all three sub-lattices, electrons,
holes, and substitutional impurities (Lines, 1977). Such a chemical defects strongly
depend on the crystal structure as well as on the chemical properties of the constituent
chemical species. The structure influences the types of lattice defects that may be formed
in significant concentrations, and also influences the mobilities of the defects and hence of
the chemical species. These mobilities determine whether or not defect equilibrium can be
achieved within pertinent times at several temperatures, and at which temperature,
during the cooling process of the material, these defects become effectively quenched. The
charges and size of the ions affect the selection of the most favored defects, and their
ability to be either oxidized or reduced determines the direction and amount of non-
stoichiometry and the resulting enhanced electronic carrier concentrations. The volatility
of a component, for instance, can also affect the equilibration and defect choice. This
aspect is of particular importance for Pb-based compounds, due to the volatility of PbO
during the synthesis of a specified material, which commonly achieves very high
treatment temperatures (Xu, 1991). Thus, for perovskites structure-type systems, the
partial substitution of A- or B-site ions promotes the activation of several conduction
mechanisms (carrier doping).
In the last few years, extensive studies have been carried out by doping at A- and/or B-site
by various researchers. It has been suggested that the introduction of different elements,
which exhibit the dissimilar electronic configuration each other, should lead to dramatic
effects associated with the electronic configuration mismatch between the ions located at the
same A- or B-site. In this way, dielectric dispersions related to a conductivity phenomenon,
which obeys the Arrhenius´s dependence, have been reported for Ba
1-x
Pb
x
TiO
3
ceramics
(Bidault et al., 1994). Dielectric anomalies at the high-temperature region have been studied
for (Pb,La)TiO
3
, BaTiO
3
and (Pb,La)(Zr,Ti)O
3
systems (Keng et al., 2003). The authors have
showed that the dielectric anomalies are related to the competition phenomenon of the
dielectric relaxation and the electrical conduction by oxygen vacancies.
Ferroelectrics

170
On the other hand, the dielectric spectra of (Ba
0.85
Sr
0.15
)TiO
3
ceramics have been study in the
paraelectric phase showing the contribution of the dc conduction to the dielectric relaxation
(Li & Fan, 2009). For KNbO
3
ceramics, the temperature and frequency dependence of the
dielectric and the conductivity properties have been studied, showing that the dielectric
relaxation can be attributed to the hopping of oxygen vacancies in the six equivalent sites in
the perovskite structure (Shing et al., 2010).
This section will show some experimental and theoretical results, for ABO
3
-type
perovskite structure systems, where the BO
6
octahedra play a critical role in the
demonstration of the ferroelectric properties. First, it will be presented the (Pb
1-
x
La
x
)(Zr
0.90
Ti
0.10
)
1-x/4
O
3
ceramic system (hereafter labeled as PLZT x/90/10), with x = 2, 4
and 6 at%, whose results has been discussed in the framework of the analysis of the effect
of oxygen vacancies on the electrical response of soft doping Pb(Zr,Ti)O
3
ceramics in the
paraelectric state (Peláiz-Barranco et al., 2008a; Peláiz-Barranco & Guerra, 2010). On the
other hand, the frequency and temperature dielectric response and the electrical
conductivity behavior around the ferroelectric–paraelectric phase transition temperature
will be presented in the (Pb
0.88
Sm
0.08
)(Ti
1−x
Mn
x
)O
3
, with x = 0, 1 and 3 at.% (named as
PSTM–x) ferroelectric ceramic system (Peláiz-Barranco et al., 2008b). In this case, the
contribution of the conductive processes to the dielectric relaxation for the studied
frequency range has been discussed considering also the oxygen vacancies as the most
mobile ionic defects in perovskites, whose concentration seems to increase with the
manganese content.
2.1 (Pb
1-x
La
x
)(Zr
0.90
Ti
0.10
)
1-x/4
O
3
ceramic system.
Figure 3 shows the temperature dependence of the real (ε’) and imaginary (ε’’) parts of the
dielectric permittivity (A and B, respectively), for the studied PLZT x/90/10
compositions, at 20 kHz. The dielectric properties results revealed no frequency
dependent dispersion of the dielectric parameters and a non-diffusive phase transition for
all the studied compositions. However, it can be observed that the temperature
corresponding to the maximum in real and imaginary dielectric permittivities (T
m
) is
strongly dependent on the lanthanum content. Additional anomalies in ε’(T) were
observed in the paraelectric phase range for low frequencies, characterize by an increase
of the dielectric parameter with the increase of the temperature (Peláiz-Barranco et al.,
2008a; Peláiz-Barranco & Guerra, 2010). Moreover, this anomaly is more pronounced
when the lanthanum content increases. As shown in the temperature dependence of the
imaginary part of the dielectric permittivity (Figure 3(B)), very high values of this
parameter are observed at the corresponding temperature range, even at not low
frequencies. Such results lead to infer that the anomalous behavior in the real dielectric
permittivity with the increase of the temperature, and the high values of ε’’, are attributed
to the same mechanism, that is to say, to the conductivity losses (Peláiz-Barranco et al.,
2008a). It can be also noted that, for the PLZT 4/90/10 and 6/90/10 compositions, the
maximum imaginary dielectric permittivity, which is associated to the paraelectric-
ferroelectric phase transition (Figure 3(B) inset), can not be easily observed as in the case
of the PLZT 2/90/10 composition. The observed behavior for the PLZT 4/90/10 and
6/90/10 compositions has been associated to the quickly increase of the losses factor
above the phase transition temperature (T
m
), which is more pronounced for such
compositions than for the PLZT 2/90/10 composition.
Dielectric Relaxation Phenomenon in Ferroelectric Perovskite-related Structures

171

Fig. 3. Temperature dependence of the real (ε’) and imaginary (ε’’) parts of the dielectric
permittivity for the PLZT x/90/10 (x = 2, 4 and 6 at%) compositions, at 20 kHz
With the increase of measurement frequency, the observed behavior in the paraelectric
phase gradually decreases, and almost disappears in the studied temperature range. Figure
4 shows the temperature dependences of ε’ and ε’’ (A and B, respectively) for the PLZT
4/90/10 composition, at several frequencies. As can be seen, the high temperature anomaly
almost disappears for the higher frequencies, showing that it could be related to a low-
frequency relaxation process. It is well known that in perovskite ferroelectrics the oxygen
vacancies could be formed in the process of sintering due to the escape of oxygen from the
lattice (Kang et al., 2003). Thus, this anomaly could be correlated with a low-frequency
relaxation process due to oxygen vacancies. Conduction electrons could be created by the
ionization of oxygen vacancies, according to the expressions (10) and (11), where V
O
, V’
O

' ''
o o
V V ' e ↔ +
(11)
The positions of the electrons depend on the structure characteristics, temperature range,
and some other factors. It was, however, shown that the oxygen vacancies lead to shallow
the electrons level. These electrons are easy to be thermally activated becoming conducting
electrons. To elucidate the physical mechanism of this behavior in the paraelectric state, the
electrical conductivity has been analyzed in the paraelectric phase (Peláiz-Barranco et al.,
2008a).
Ferroelectrics

172

Fig. 4. Temperature dependence of the real (ε’) and imaginary (ε’’) parts of the dielectric
permittivity, at several frequencies for the PLZT 4/90/10 composition
By using the Jonscher’s relation expressed on the equation (7), the frequency dependence of
the electrical conductivity for the studied compositions was analyzed in the paraelectric
state, at several temperatures (Peláiz-Barranco et al., 2008a). The temperature dependence of
the dc conductivity and the hopping frequency also followed an Arrhenius’ behavior,
according to the equations (8) and (9), respectively. The obtained activation energy values
for both cases are shown in the Table 1.

Composition U
dc
(eV) U
H
(eV)
PLZT 2/90/10 0.56 1.21
PLZT 4/90/10 0.49 1.15
PLZT 6/90/10 0.46 0.99
Table 1. Activation energy values for dc conductivity contribution, U
dc
, and the hopping
process, U
H
, for the studied compositions (Peláiz-Barranco et al., 2008a)
According to the obtained results, some considerations can be taken into account in order to
explain the observed behaviors. It is well known that during the synthesis and process of the
ceramic system, i.e. the powders calcinations and the sintering stages, especially for the
Pb(Zr,Ti)O
3
system (PZT), there exists a high volatility of lead oxide because of the high
temperatures operation. Such lead volatilization provides both fully-ionized cationic lead
(V’’
Pb
) vacancies and anionic oxygen vacancies (V’’
O
). On the other hand, following the
Eyraud’s model (Eyraud et al., 1984; Eyraud et al., 2002), it is assumed that the lanthanum
Dielectric Relaxation Phenomenon in Ferroelectric Perovskite-related Structures

173
valence, as doping in the PZT system, has a strong influence in the ionization state of
extrinsic lead and oxygen vacancies. In order to compensate the charge imbalance, one La
3+

ion occupying a Pb
2+
site (on the A-site of the perovskite structure) generates one half of
singly ionized lead vacancies (V’
Pb
) rather than one doubly ionized vacancy (V’’
Pb
). Thus, in
the studied PLZT x/90/10 compositions it should be considered different types of defects,
related to V’
Pb
, V’’
Pb
, V’
O
and V’’
O
vacancies, whose contribution depends on the analyzed
temperature range. A very low concentration of neutral lead and oxygen vacancies are
considered around and above the room temperature.
At low temperatures, the lead vacancies are quenched defects, which are difficult to be
activated. They could become mobile at high temperatures with activation energy values
around and above 2 eV (Guiffard et al., 2005). However, to the best of our knowledge the
ionization state of lead vacancies remains unknown. On the other hand, it has been reported
(Verdier et al., 2005; Yoo et al., 2002) that the oxygen vacancies exist in single ionized state
with activation energy values in the range of 0.3–0.4 eV. For Pb-based perovskite
ferroelectrics, activation energies values in the range of 0.6–1.2 eV are commonly associated
to doubly-ionized oxygen vacancies (Smyth, 2003; Moos et al., 1995; Moos & Härdtl, 1996).
For PLZT 4/90/10 and PLZT 6/90/10 compositions, the results have suggested that the dc
conductivity could be related to single ionized states (V’
O
). For the PLZT 2/90/10
composition, a higher activation energy value suggests a lower oxygen vacancies
concentration (Steinsvik et al., 1997), whose values are closer to those values associated to
doubly-ionized oxygen vacancies (V’’
O
) (Smyth, 2003; Moos et al., 1995; Moos & Härdtl,
1996). Thus, the dc conductivity is assumed to be produced according to the reaction given
by the expression (11), decreasing the number of V’
O
, which could contribute for the lower
anomaly observed for the PLZT 2/90/10 composition. The released electrons may be
captured by Ti
4+
and generates a reduction of the valence, following the relation (12).

4 3
' Ti e Ti
+ +
+ ↔ (12)
Thus, the conduction process can occur due to the hopping of electrons between Ti
4+
and
Ti
3+
, leading to the contribution of both single and doubly-ionized oxygen vacancies and the
hopping energy between these localized sites for the activation energy in the paraelectric
phase region for the studied PLZT compositions.
Considering the oxygen vacancies as the most mobile defects in the studied PLZT
compositions, it has been analyzed their influence on the dielectric relaxation processes
(Peláiz-Barranco et al., 2008a; Peláiz-Barranco & Guerra, 2010). It is known that the
spontaneous polarization originating from the ionic or dipoles displacement contributions is
known to be the off-center displacement of Ti
4+
ions, from the anionic charge center of the
oxygen octahedron for the PLZT system (Xu, 1991). The presence of oxygen vacancies
would distort the actual ionic dipoles due to the Ti
4+
ions. The decay of polarizations due to
the distorted ionic dipoles could be the cause for the dielectric relaxation processes.
However, usually the activation energy values associated to the relaxations involving
thermal motions of Ti
4+
(Peláiz-Barranco & Guerra, 2010) are higher than those observed in
the studied PLZT x/90/10 compositions , showing that it should not be a probable process.
The obtained U
H
values have suggested that the hopping process could be related to the
doubly-ionized oxygen vacancies motion (Smyth, 2003; Moos et al., 1995; Moos & Härdtl,
1996). The short-range hopping of oxygen vacancies, similar to the reorientation of the
dipoles, could lead to the dielectric relaxation.
Ferroelectrics

174
On the other hand, the frequency and temperature behavior of the complex dielectric
permittivity was analyzed (Peláiz-Barranco & Guerra, 2010) considering the Cole–Cole
model, given by equations (4) and (5). The main relaxation time, obtained by the fitting by
using both equations, followed the Arrhenius dependence (equation (6)) in the studied
temperature range. The activation energy values for the relaxation processes are shown in
Table 2 (Peláiz-Barranco & Guerra, 2010). The results have been associated with ionized
oxygen vacancies. Thus, following the previously discussion, the dielectric relaxation
phenomenon could be related to the short-range hopping of oxygen vacancies.

Composition Ea (eV)
PLZT 2/90/10 0.48
PLZT 4/90/10 0.40
PLZT 6/90/10 0.37
Table 2. Activation energy values of the relaxation process for the studied compositions
(Peláiz-Barranco & Guerra, 2010)
2.2 (Pb
0.88
Sm
0.08
)(Ti
1-x
Mn
x
)O
3
ceramic system.
Figure 5 depicts the temperature dependence of ε’ and ε’’ for the PSTM–x samples, for three
selected frequencies, as example of the investigated behavior for the whole frequency range.
Two peaks or inflections were observed for the real part of the dielectric permittivity at the
studied frequency range. The first one, which was observed around 340
o
C for all the
compositions, was associated to the temperature of the paraelectric-ferroelectric phase
transition (T
m
), according to previous reports for these materials (Takeuchi et al., 1983;
Takeuchi et al., 1985). For all the cases, the paraelectric-ferroelectric phase transition
temperature (T
m
) did not show any frequency dependence, which is typical of ‘normal’
paraelectric-ferroelectric phase transitions (Xu, 1991). On the other hand, the imaginary
dielectric permittivity showed a peak at the same temperature, to that observed for the real
part of the dielectric permittivity (T
m
), confirming the ‘normal’ characteristic of the phase
transition. In fact, not frequency dispersion of the temperature of the maximum dielectric
permittivity was observed. However, a sudden increase of ε’’ was obtained for temperatures
around 400
o
C for all the studied compositions, which could be associated to high
conductivity values that promote the increase of the dielectric losses.
The presence of two peaks in the temperature dependence of ε’ has been observed in
(Pb
0.88
Ln
0.08
)(Ti
0.98
Mn
0.02
)O
3
(being Ln = La, Nd, Sm, Gd, Dy, Ho, Er) ferroelectric ceramics
(Pérez-Martínez et al., 1997; Peláiz-Barranco et al., 2009a). In this way, for small-radius-size
ions (Dy, Ho and Er) a strong increase of the tetragonality has been observed (Pérez-
Martínez et al., 1997), even for values higher than those observed for pure lead titanate. Both
peaks were associated to paraelectric-ferroelectric phase transitions concerning two different
contributions to the total dielectric behavior of the samples; one, on which the rare earths
ions occupy the A-sites and the other one where the ions occupy the B-sites of the perovskite
structure (Pérez-Martínez et al., 1997). For high-radius-size ions (La, Nd, Sm and Gd) the
analysis has shown that, even when it could be possible an eventual incorporation of the
rare earth into the A- and/or B-sites of the perovskite structure, both peaks could not be
associated to the paraelectric-ferroelectric phase transitions. In this case, the observed peak
at lower temperatures has been associated to the paraelectric-ferroelectric phase transition,
whereas the hopping of oxygen vacancies has been considered as the cause for the dielectric
anomaly at higher temperatures (Peláiz-Barranco et al., 2009a).
Dielectric Relaxation Phenomenon in Ferroelectric Perovskite-related Structures

175

Fig. 5. Temperature dependence of the real (ε’) and imaginary (ε’’) parts of the dielectric
permittivity for the PSTM-0 (A), PSTM-1 (B) and PSTM-3 (C) compositions
Considering these results, two studies were carried out on these samples; the first one
(Peláiz-Barranco et al., 2008b) concerning the dielectric relaxation phenomenon and the
electrical conductivity behavior for temperatures around the paraelectric-ferroelectric phase
transition (around 340
o
C); the second one concerning the electrical conductivity behavior
around the second peak (Peláiz-Barranco & González-Abreu, 2009b).
The frequency dependence of the ε’ and ε’’ for the studied PSTM-x compositions below T
m

(Peláiz-Barranco et al., 2008b) was analyzed by using the Cole-Cole model (equations (4) and
(5)). The temperature dependence for the mean relaxation times, obtained from the fitting of
the experimental data by using equations (4) and (5) revealed an Arrhenius’ behavior,
according to the equation (6). The obtained values for the activation energy were 0.89 eV, 0.81
eV and 0.62 eV, for the PSTM-0, PSTM-1 and PSTM-3 compositions, respectively, which clearly
show that the dielectric relaxation processes in the studied samples are closely related to the
oxygen vacancies, which have been reported as the most mobile ionic defects in perovskites
(Poykko & Chadi, 2000). According to previously reported results (Steinsvik et al., 1997), the
activation energy for ABO
3
perovskites decreases with the increase of the oxygen vacancies
content. As observed, the activation energy values for the studied samples decreases with the
increase of the manganese content, which suggests an increase of oxygen vacancies
concentration (Steinsvik et al., 1997). On the other hand, previous studies on electronic
paramagnetic resonance (EPR) in earth rare and manganese modified lead titanate ceramics,
have shown that a Mn
4+
/Mn
2+
reduction takes place during the sintering process (Ramírez-
Rosales et al., 2001). As a consequence, oxygen vacancies have to be created to compensate for
the charge imbalance. The increase of manganese content should promote a higher
concentration of oxygen vacancies, which agrees with the decrease of activation energy values.
Similarly to the results obtained for the PLZT x/90/10 ceramics, the obtained activation
energy values for the PSTM-x compositions were found to be lower that those for relaxations
involving thermal motions of Ti
4+
(Maglione & Belkaoumi, 1992). So that, the observed
Ferroelectrics

176
relaxation process for the studied ceramics could be attributed to the decay of polarization in
the oxygen defect-related dipoles due to their hopping conduction.
In order to better understand the conduction mechanism related to the observed relaxation
process, the experimental data for the PSTM-x compositions were fitted by considering the
equations (7), (8) and (9). Results of the dc conductivity (σ
dc
) and the hopping frequency
(ω
H
) are shown in the Figure 6, for temperatures below T
m
. The solid lines on Figures 6(A)
and 6(B), represent the fitting using the equations (8) and (9), respectively. The obtained
activation energy values (for dc conductivity contribution, U
dc
, and the hopping process,
U
H
) are shown in the Table 3.

Fig. 6. Arrhenius’ dependence for the dc conductivity (σ
dc
) and the hopping frequency (ω
H
)
(A and B, respectively), below T
m,
for the studied PSTM-x compositions
As can be seen, the activation energy values for the dc conductivity are very close to the
activation energy values of the ionic conductivity by oxygen vacancies in perovskite type
ferroelectric oxides (Jiménez & Vicente, 1998; Bharadwaja & Krupanidhi, 1999; Chen et al.,
2000; Smyth, 2003). Thus, it can be concluded that oxygen vacancies are the most likely
Dielectric Relaxation Phenomenon in Ferroelectric Perovskite-related Structures

177
charge carriers operating in these ceramics below T
m
. At room temperature, the oxygen
vacancies exhibit a low mobility, whereby the ceramic samples exhibit an enhanced
resistance. However, with rising temperature, they are activated and contribute to the
observed electrical behavior. In addition, the dielectric relaxations occurring at low
frequency are related to the space charges in association with these oxygen vacancies, which
can be trapped at the grain boundaries or electrode-sample interface.
On the other hand, the activation energy values for the hopping processes (U
H
) are not very
far from the U
dc
values, showing that the hopping processes could be related to the
movement of the oxygen vacancies. The short-range hopping of oxygen vacancies, similar to
the reorientation of the dipole, could lead to the relaxation processes.
For temperatures above T
m
, i.e. in the paraelectric phase, it was carried out the same analysis
in the studied samples (Peláiz-Barranco et al., 2008b). The electrical conduction was
associated with the doubly ionized oxygen vacancies and the relaxation processes were
related to the distorted ionic dipoles by the oxygen vacancies.
Concerning the second peak (Peláiz-Barranco & González-Abreu, 2009b), a detailed study of
the electrical conductivity behavior was carried out by using the Jonscher´s formalism. The
electrical conduction was associated to the doubly-ionized oxygen vacancies and its
influence on the relaxation processes was analyzed.
3. Bi-layered ferroelectric perovskites.
The materials of the Bi–layered structure family were first described by Aurivillius in 1949.
The corresponding general formula is [Bi
2
O
2
]
2+
[A
n−1
B
n
O
3n+1
]
2−
, where A can be K
+
, Sr
2+
, Ca
2+
,
Ba
2+
, Pb
2+
, etc.; B can be Ti
4+
, Nb
5+
, Ta
5+
, W
6+
, etc., and n is the number of corner sharing
octahedral forming the perovskite like slabs, which is usually in the range 1-5. The oxygen
octahedra blocks, responsible for ferroelectric behavior, are interleaved with (Bi
2
O
2
)
2+
layers
resulting in a highly anisotropic crystallographic structure where the c parameter, normal to
(Bi
2
O
2
)
2+
layers, is much greater than a and b parameters of the orthorhombic cell. For this
family, ferroelectricity is strongly depending on the crystallographic orientation of the
materials, being the aim of continuing research (Lee et al, 2002; Watanabe et al., 2006). It is
well-known that these have the majority polarization vector along the a-axis in a unit cell
and that the oxygen vacancies prefer to stay in the Bi
2
O
2
layers, where their effect upon the
polarization is thought to be small, and not in the octahedral site that controls polarization.
The layered perovskites are considered for nonvolatile memory applications because of the
characteristics of resistance to fatigue (Chen et al., 1997). The frequency response of
SrBi
2
Ta
2
O
9
and SrBi
2
Nb
2
O
9
ceramics has been studied considering the bulk ionic
conductivity to evaluate the electrical fatigue resistance. The results have showed much
higher conductivity values than those of the PZT perovskite ferroelectrics, which has been
considered as the cause of the good fatigue resistance. There is an easy recovery of the
oxygen vacancies from traps, which limits the space charge generated during the
polarization reversal process.
An interesting feature of these materials is that some of them allow cation site mixing
among atoms positions (Mahesh Kumar & Ye, 2001), especially between the bismuth and
the A-site of the perovskite block (Blake et al., 1997). For example, it has been reported
(Ismunandar & Kennedy, 1999) that both Sr
2+
and Ba
2+
can occupy the Bi sites in ABi
2
Nb
2
O
9

(A=Sr,Ba). For the studied materials, the degree of disorder is related to the change in the
cell volume, which is much lower than that reported in PbBi
2
Nb
2
O
9
. For SrBi
2
Ta
2
O
9
(Mahesh
Ferroelectrics

178
Kumar & Ye, 2001), the substitution of Fe
3+
for Sr
2+
increases the ferroelectric-paraelectric
transition temperature and provides a higher resistivity value. However, the substitution of
Ca
2+
for Bi
3+
in the bismuth layers increases the electrical conductivity.
The Aurivillius family exhibit a dielectric behavior characteristic for ferroelectric relaxors
(Miranda et al., 2001; Kholkin et al., 2001), e.g. i) marked frequency dispersion in the vicinity
of temperature (T
m
) where the real part of the dielectric permittivity (ε’) shows its maximum
value, ii) the temperature of the corresponding maximum for ε’ and the imaginary part of
the dielectric permittivity (ε’’) appears at different values, showing a frequency dependent
behavior, iii- the Curie-Weiss law is not fulfilled for temperatures around T
m
. The materials
have attracted considerable attention due to their large remanent polarization, lead-free
nature, relatively low processing temperatures and other characteristics (Miranda et al.,
2001; Kholkin et al., 2001; Lee et al, 2002; Nelis et al, 2005; Huang et al., 2006; Watanabe et
al., 2006). The origin of the relaxor behavior for these materials has been associated to a
positional disorder of cations on A or B sites of the perovskite blocks that delay the
evolution of long-rage polar ordering (Miranda et al., 2001).
For BaBi
2
Nb
2
O
9
ceramics (Kholkin et al., 2001), it has been studied the frequency relaxation
of the complex dielectric permittivity in wide temperature and frequency ranges. The
reported relaxation time spectrum is qualitative difference from that of conventional relaxor
ferroelectrics; this shifts rapidly to low frequencies on cooling without significant
broadening. It has been discussed considering a reduced size of polarization clusters and
their weak interaction in the layered structure.
For bismuth doped Ba
1-x
Sr
x
TiO
3
ceramics, it has been showed that the Bi
3+
doping decreases
the maximum of the real part of the dielectric permittivity, whose temperature also shifts to
lower temperatures for the lower Sr
2+
concentrations (Zhou et al, 2001). A relaxor behavior
has been reported for these ceramics, suggesting a random electric field as the responsible of
the observed behavior.
The complex dielectric permittivity spectrum in the THz region was studied in SrBi
2
Ta
2
O
9

films (Kadlec et al., 2004). The lowest-frequency optical phonon revealed a slow monotonic
decrease in frequency on heating with no significant anomaly near the phase transitions. The
dielectric anomaly near the ferroelectric phase transition was discussed considering the
slowing down of a relaxation mode. It was also discussed the loss of a centre of symmetry in
the ferroelectric phase and the presence of polar clusters in the intermediate ferroelastic phase.
For BaBi
4
Ti
4
O
15
ceramics (Bobić et al., 2010), the dielectric relaxation processes have been
described by using the empirical Vogel–Fulcher law. The electrical conductivity behavior
has suggested that conduction in the high-temperature range could be associated to oxygen
vacancies.
The previous results correspond to part of the studies carried out in the last years
concerning the dielectric and electrical conductivity behaviors of Bi–layered structure
materials. However, a lot of aspects of these remain unexplored, especially concerning the
dielectric relaxation phenomenon and the conductivity mechanisms. It has been the
motivation of the present authors, and other colleagues, to study the dielectric relaxation in
one of these systems.
3.1 Sr
1-x
Ba
x
Bi
2
Nb
2
O
9
ceramic system.
It has been previously commented that SrBi
2
Nb
2
O
9
is a member of the Aurivillius family
(Blake et al., 1997; Ismunandar & Kennedy, 1999; Haluska & Misture, 2004; Nelis et al., 2005;
Dielectric Relaxation Phenomenon in Ferroelectric Perovskite-related Structures

179
Huang et al, 2006), consisting of octahedra in the perovskite blocks sandwiched by two
neighboring (Bi
2
O
2
)
2+
layers along the c-axis in a unit cell. The divalent Sr
2+
cation located
between the corner-sharing octahedra can be totally or partially replaced by other cations,
most commonly barium (Haluska & Misture, 2004; Huang et al, 2006). The barium modified
SrBi
2
Nb
2
O
9
ceramics have showed that the incorporation of Ba
2+
in the Sr
2+
sites (A sites of
the perovskite) provides a complex dielectric response showing a transition from a normal
to a relaxor ferroelectric (Huang et al, 2006). On the other hand, it has been analyzed the
barium preference for the bismuth site, which occur to equilibrate the lattice dimensions
between the (Bi
2
O
2
)
2+
layers and the perovskite blocks (Haluska & Misture, 2004).

Fig. 7. Temperature dependence of the real (ε’) and imaginary (ε’’) parts of the dielectric
permittivity for A)- Sr
0.5
Ba
0.5
Bi
2
Nb
2
O
9
and B)- Sr
0.1
Ba
0.9
Bi
2
Nb
2
O
9
, at various frequencies
Sr
1-x
Ba
x
Bi
2
Nb
2
O
9
ferroelectric ceramics were analyzed in a wide frequency range (100 Hz to 1
MHz) for temperatures below, around and above the temperature where the real part of the
dielectric permittivity showed a maximum value. Three compositions were considered, i.e.
x=50, 70 and 90 at%. Typical characteristics or relaxor ferroelectrics were observed in the
studied samples (González-Abreu et al., 2009; González Abreu, 2010). Figure 7 shows the
temperature dependence of the real (ε’) and imaginary (ε’’) parts of the dielectric
permittivity for Sr
0.5
Ba
0.5
Bi
2
Nb
2
O
9
and Sr
0.1
Ba
0.9
Bi
2
Nb
2
O
9
, at various frequencies, as example
of the observed behavior in the studied frequency range for the three compositions. On the
other hand, an important influence of the electrical conductivity mechanisms was
considered from the temperature dependence of the imaginary part of the dielectric
permittivity, which increases with temperature, especially for the lower frequencies.
The origin of the relaxor behavior for these ceramics has been explained by considering a
positional disorder of cations on A or B sites of the perovskite blocks that delay the
Ferroelectrics

180
evolution of long-range polar ordering (Miranda et al., 2001). For Ba
2+
doped SrBi
2
Nb
2
O
9
ceramics, a higher frequency dependence of the dielectric parameters has been observed
than that of the undoped SrBi
2
Nb
2
O
9
system (González Abreu, 2010). The results have been
discussed by considering the incorporation of a bigger ion into the A site of the perovskite
block. The Ba
2+
ions not only substitute the Sr
2+
ions in the A-site of the perovskite block but
enter the (Bi
2
O
2
)
2+
layers leading to an inhomogeneous distribution of barium and local
charge imbalance in the layered structure.
Following the Cole-Cole model (Cole & Cole, 1941), the real and imaginary part of the
dielectric permittivity were fitted by using equations (4) and (5) in a wide temperature range
(González-Abreu et al., 2009; González Abreu, 2010). Figures 8 and 9 show the experimental
data (solid points) and the corresponding theoretical results (solid lines) at a few
representative temperatures for Sr
0.5
Ba
0.5
Bi
2
Nb
2
O
9
and

Fig. 8. Frequency dependence of the real ε’ (•) and imaginary ε’’ (●) parts of the dielectric
permittivity, at a few representatives temperatures, for Sr
0.5
Ba
0.5
Bi
2
Nb
2
O
9
. Solid lines
represent the fitting by using equations (4) and (5)
Two relaxation processes were evaluated for the studied compositions from the temperature
dependence of the relaxation time (González-Abreu et al., 2009; González Abreu, 2010),
which was obtained from the fitting by using the Cole-Cole model. The first one takes place
around the temperature range where the high dispersion of the real part of the dielectric
permittivity was observed (see Figure 7), i.e. below and around the region where the
maximums of ε´ are obtained in the studied frequency range. The temperature dependence
Dielectric Relaxation Phenomenon in Ferroelectric Perovskite-related Structures

181
of the relaxation time was found that follows the Vogel-Fulcher law (González-Abreu et al.,
2009; González Abreu, 2010), which describes the typical temperature dependence of the
relaxation time for relaxor ferroelectrics. From this point of view, it could be considered that
the main origin of the first dielectric relaxation process could be associated to the relaxor-
like ferroelectric behavior of the studied ceramics.

Fig. 9. Frequency dependence of the real ε’ (•) and imaginary ε’’ (●) parts of the dielectric
permittivity, at a few representatives temperatures, for Sr
0.1
Ba
0.9
Bi
2
Nb
2
O
9
. Solid lines
represent the fitting by using equations (4) and (5)
The temperature dependence of the relaxation time for second relaxation process was fitted
by using the known Arrhenius law given by equation 6 (González-Abreu et al., 2009;
González Abreu, 2010). This second process was observed for temperatures where an
important contribution of the electrical conductivity mechanisms was considered from the
temperature dependence of the imaginary part of the dielectric permittivity. It is known that
Ba
2+
ions could occupy the A-sites at the octahedra in the perovskite blocks and the bismuth
site in the layered structure for Sr
1-x
Ba
x
Bi
2
Nb
2
O
9
ceramics (Haluska & Misture, 2004). The
electrical charge unbalance caused by the trivalent Bi
3+
ion substitution for the divalent Ba
2+

ions is compensated by the creation of oxygen vacancies. Then, it could be suggested that
the hopping of the electrons, which appears due to the ionization of the oxygen vacancies,
could contribute to the dielectric relaxation and its long-distance movement contributes to
the electrical conduction.
However, other important contribution should be considered. For relaxor ferroelectrics,
microdomains can be observed even at temperature regions far from the region where the
Ferroelectrics

186
Zhou, L.; Vilarinho, P. M. & Baptista, J. L. (2001). Dielectric properties of bismuth doped Ba
1-
x
Sr
x
TiO
3
ceramics. Journal of European Ceramic Society, 21 (April 2001) 531-534, ISSN
0955-2219.
11
The Ferroelectric-Ferromagnetic Composite
Ceramics with High Permittivity and
High Permeability in Hyper-Frequency
Yang Bai
The University of Science and Technology Beijing
China
1. Introduction
With the rapid development of portable electronic products and wireless technology, many
electronic devices have evolved into collections of highly integrated systems for multiple
functionality, faster operating speed, higher reliability, and reduced sizes. This demands the
multifunctional integrated components, serving as both inductor and capacitor. As a result,
low temperature co-fired ceramics (LTCC) with integrated capacitive ferroelectrics and
inductive ferrites has been regarded as a feasible solution through complex circuit designs.
However, in the multilayer LTCC structure consisting of ferroelectrics and ferrites layers,
there are always many undesirable defects, such as cracks, pores and cambers, owing to the
co-firing mismatch between different material layers, which will damage the property and
reliability of end products (Hsu & Jean, 2005). A single material with both inductance and
capacitance are desired for true integration in one element. For example, if the materials
with both high permeability and permittivity are used in the anti electromagnetic
interference (EMI) filters, the size of components can be dramatically minimized compared
to that of conventional filters composed of discrete inductors and capacitors. Because little
single-phase material in nature can meet such needs (Hill, 1999), the development of
ferroelectric-ferromagnetic composite ceramics are greatly motivated.
Many material systems, such as BaTiO
3
/ NiCuZn ferrite, BaTiO
3
/ MgCuZn ferrite,
Pb(Zr
0.52
Ti
0.48
)O
3
/ NiCuZn ferrite, Pb(Mg
1/3
Nb
2/3
)O
3
-Pb(Zn
1/3
Nb
2/3
)O
3
-PbTiO
3
/ NiCuZn
ferrite and Bi
2
(Zn
1/3
Nb
2/3
)
2
O
7
/ NiCuZn ferrite, were investigated and found exhibit fine
dielectric and magnetic properties. In these reports, spinel ferrites, such as NiCuZn ferrite,
were always used as the magnetic phase of composite ceramics, because they are mature
materials for LTCC inductive components. However, the cut-off frequency of spinel ferrites
is limited below 100MHz by the cubic crystal structure, so the resulting composite ceramics
can not be used in hyper-frequency or higher frequency range. To keep up with the trend
towards higher frequency for electronic technology, hexagonal ferrites, including Y-type
hexagonal ferrite Ba
2
Me
2
Fe
12
O
22
and Z-type hexagonal ferrite Ba
3
Me
2
Fe
24
O
41
(Me=divalent
transition metal), should be used in the composite ceramics.
Co
2
Z hexagonal ferrite has high permeability and low loss in hyper-frequency, but the very
high sintering temperature (>1300
o
C) works against its application in LTCC. Y-type
hexagonal ferrite has a bit lower permeability, but the excellent sintering behavior makes it a
Ferroelectrics

188
good candidate of magnetic material in LTCC. To achieve high dielectric permittivity, lead-
based relaxor ferroelectric ceramics is a good choice as the ferroelectric phase in the
composite ceramics owing to its high dielectric permittivity and low sintering temperature.
In this chapter, we summarize the co-firing behavior, microstructure and electromagnetic
properties of the composite ceramics for hyper-frequency. The material system is mainly
focused on a composite ceramics composed of 0.8Pb(Ni
1/3
Nb
2/3
)O
3
-0.2PbTiO
3
(PNNT) and
Ba
2
Zn
1.2
Cu
0.8
Fe
12
O
22
(BZCF), which has excellent co-firing behavior and good
electromagnetic properties in hyper-frequency, and some other composite ceramics are also
involved in some sections.
2. The co-firing behavior, phase composition and microstructure
2.1 The co-firing behavior and densification
Due to the different sintering temperatures and shrinkage rates of ferroelectric phase and
ferromagnetic phase, remarkable co-firing mismatch often occurs and results in undesirable
defects, such as cracks and cambers. As a result, the property of composite ceramics and the
reliability of end products are damaged. Thanks to the existence of large amount of grain
boundaries to dissipate stress, the composite ceramics with powder mixture have much
better co-firing behavior than the multilayered composite ceramics. Although the mismatch
of densification rate is alleviated to a larger extent, a good sintering compatibility between
ferroelectric and ferromagnetic grains is still required for better co-firing match. The starting
temperature of shrinkage and the point of maximum shrinkage rate are both important for
the co-firing behavior of composite ceramics. Some research indicates that the composite
ceramics exhibits an average sintering behavior between two phases and the shrinkage rate
curve of composite ceramics is between those of two component phases (Qi et al., 2008).

Fig. 1. The density of the sintered PNNT-BZCF composite ceramics as a function of the
weight fraction of ferroelectric phase
Y-type hexagonal ferrite has a lower sintering temperature of 1000~1100
o
C, which is similar
to that of lead-based ferroelectric ceramics. For example, in PNNT-BZCF composite
material, BZCF has a sintering temperature of 1050
o
C, same as that of PNNT. Hence, the
composite system has good co-firing behavior for each composition (Bai et al., 2007). After
sintered at 1050
o
C, all the samples exhibit a high density, above 95% of theoretical density.
Fig. 1 shows the composition dependence of the density of sintered PNNT-BZCF composite
The Ferroelectric-Ferromagnetic Composite Ceramics with High Permittivity
and High Permeability in Hyper-Frequency

189
ceramics. Since the density of a composite material is the weighted average of those of
constituent phases, it increases linearly with the rise of weight fraction of ferroelectric phase.
Similar relationship is obtained in other composite materials (Qi et al., 2004 & Shen et al.,
2005).
2.2 The element diffusion
The element diffusion always occurs between two phases during the sintering process at
high temperature. The thickness of diffusion layer and element distribution influence
microstructure and properties of composite ceramics. The diffusion coefficient is determined
by the ion’s radius and charge. Table 1 shows the radius of some ions commonly used in
ferroelectric ceramics and ferrite.

Ba
2+
Pb
2+
Ti
4+
Nb
5+
Fe
3+
Fe
2+
Co
2+
Zn
2+
Cu
2+
Mn
3+
Ni
2+

0.135 0.120 0.068 0.07 0.076 0.064 0.074 0.074 0.072 0.066 0.072
Table 1. The radius of some ions
It is always thought that Ba
2+
ion does not diffuse due to the large radius, which has been
confirmed by experiments. Although Pb
2+
also has large radius, the low vapor pressure
make it to easily escape from lattice at high temperature. The deficiency of Pb
2+
in the lattice
can result in the formation of pyrochlore phase. For the metallic ion in ferrite, the diffusion
coefficient can be ranked as D
Co
>D
Fe
>D
Zn
>D
Ni
,D
Cu
based on the experiments of atomic
emission spectrometry (AES) and electron probe micro-analyzer (EPMA). Fig. 2 (a) and (b)
show the backscattered electron image and element distribution around the interface in the
composite ceramics consisting of Pb(Mg
1/3
Nb
2/3
)O
3
and NiCuZn ferrite. The diffusion of
different ions between ferroelectric grain and ferromagnetic grain is clear.

Fig. 2. (a) the backscattered electron image and (b) element distribution around the interface
of the composite ceramics of Pb(Mg
1/3
Nb
2/3
)O
3
-NiCuZn ferrite
The element diffusion can influence the microstructure and electromagnetic properties of
composite ceramics. For example, the grains at the interface of two phases may grow
abnormally large. To alleviate the element diffusion, lowering the sintering temperature is a
feasible solution.
Ferroelectrics

190
2.3 Phase composition crystal structure
During the co-firing process, chemical reactions may take place at the interface of two
phases and produce some new phases, which affect the properties of co-fired composite
ceramics. For example, pyrochlore phase is often formed in the composite ceramics with
lead-based ferroelectric ceramics due to Pb volatilization. Fig. 3 shows a X-ray diffraction
(XRD) spectrum of the composite ceramics of 40wt%PbMg
1/3
Nb
2/3
O
3
-60wt%NiCuZn ferrite,
which clearly shows the existence of pyrochlore phase. If the sintering temperature is
lowered below 1000
o
C, the volatilization of Pb can be largely reduced, so does the formation
of pyrochlore phase.

Fig. 3. XRD spectrum of the composite ceramics of 40wt%PbMg
1/3
Nb
2/3
O
3
-60wt%NiCuZn
ferrite
Fig. 4 compares the XRD spectra of PNNT-BZCF composite ceramics before and after
sintering process. According to the XRD spectra, no other phase is found after co-firing
process, i.e. no obvious chemical reaction takes place between PNNT and BZCF during the
sintering process of 1050
o
C.
It is clear that only perovskite phase can be detected in the XRD spectra of samples either
before or after co-firing process, if the weight fraction of PNNT is higher than or equals to
0.8. It is because that the crystal structure of Y-type hexagonal ferrite is more complex than
the perovskite structure of ferroelectric phase, which results in a much lower electron
density. In addition, for the sample with same volume fraction of PNNT and BZCF, the XRD
intensity of perovskite phase is much stronger than that of BZCF due to the same reason.
With the rise of BZCF amount, the intensities of its diffraction peaks gradually enhance. Up
to the weight fraction of ferroelectric phase is as low as x=0.1, the XRD peaks of perovskite
phase are still obvious in the XRD spectrum.
The crystal morphology and orientation may be changed due to the different densification
characters of two phases in the co-firing process (Bai et al., 2009). It is noticed from Fig. 4
that the relative intensity of the diffraction peaks of Y-type hexagonal ferrite changes after
the co-firing process. For the green samples, the primary diffraction peak of BZCF is at 30.4
o

corresponding to (110) plane, which is same as the pure Y-type hexagonal ferrite; while the
primary peak is at 32
o
corresponding to (1013) plane for the sintered samples, which is the
secondary peak of pure Y-type hexagonal ferrite. This variation of XRD intensities of Y-type
hexagonal ferrite after co-firing process is well indexed by comparing the sintered samples
of x=0 and x=0.1 in Fig. 5. The change reflects a lattice distortion induced by the internal
stress.
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193
Fig. 6 (a)–(f) show the scanning electron microscope (SEM) images of the microstructure of
PNNT-BZCF composite ceramics. In backscattered electron image, the grains of PNNT and
BZCF respectively appear white and gray due to the difference of molecular weights of the
elements in them. The sintered samples exhibit dense microstructures for each composition
and the grains of PNNT and BZCF distribute homogeneously. It indicates that this
composite system has a fine co-firing behavior over a wide composition range, which thanks
to the same sintering temperature of PNNT and BZCF.
The average size of ferroelectric or ferrite grains decreases with the rise of corresponding
phase amount. For example, as BZCF content is low, few ferrite grains are besieged by large
amount of PNNT grains. It becomes difficult for small ferrite grains to merge with the
neighboring likes. With the increase of ferrite’s content, the chance of amalgamation of small
grains rises, and then grains grow larger. The thing is same for PNNT grains.
From the SEM images, it is noticed that the grain morphology of ferrite changes obviously
with composition. In the sample of pure Y-type hexagonal ferrite (x=0), the grains are
platelike and many of them are of hexagonal shape [Fig. 6 (a)]. In the co-fired ceramics [Fig.
6(b)-(f)], the planar grains of hexagonal ferrite become equiaxed crystals just as those
ferroelectric grains. During the co-firing process, the grain growth of two constituent phases
is affected each other. Because equiaxed crystal is more favorable for a compact-stack
microstructure than planar crystal, the surrounding equiaxed grains of PNNT modulate the
grain growth of BZCF particles and assimilate their grain shape into equiaxed crystal during
the co-firing process. It is well known that the internal stress is unavoidable in the co-fired
ceramics. In BZCF-PNNT composite ceramics, the compact-stacked grains and the change of
BZCF’s grain morphology suggest the existence of internal stress and lattice distortion,
which are also reflected in XRD spectra as discussed in prior section.
3. The static electromagnetic properties
3.1 The ferroelectric hysteresis loop
For the ferroelectric-ferromagnetic composite ceramics, the ferroelectric or ferromagnetic
character is determined by the corresponding phase, while the magnetoelectric effect is
always weak. To examine the ferroelectricity of composite ceramics, the ferroelectric
polarization–electric field (P-E) hysteresis loop is the most important character.
For PNNT-BZCF composite ceramics, the P-E hysteresis loops are observed over the whole
composition range (Fig. 7), which implies the ferroelectric nature of composite ceramics. The
maximum polarization P
max
decreases with the reduction of ferroelectric phase due to
dilution effect, which indicates that the ferroelectricity of composite ceramics originates
from the nature of ferroelectric phase.
It is also noted that the shape of P-E loop varies with composition. The sample with high
PNNT amount (x>0.8) has fine and slim hysteresis loop, while the sample with relative less
ferroelectric phase has an open-mouth-shaped P-E loop. It is because that the ferrite has
much lower electric resistivity of about 10
6
Ω cm than that of ferroelectric ceramics (above
10
11
Ω cm). In the ferroelectric-ferromagnetic composite ceramics, the ferrite grains serve as
a conductive phase in the electric measurement, especially under a high electric field. If the
ferrite content is low, the small ferrite grains are besieged by the ferroelectric grains with
high resistivity and there is no conductive route in the microstructure. As a result, the
composite ceramics has high resistivity and low leak current. With the rise of ferrite amount,
the percolation occurs in the composite system and the resistivity drops remarkably (Qi et
al., 2004 & Bai et al., 2007). The large leak current results in an open-mouth-shaped P-E loop.
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194

Fig. 7. P-E hysteresis loops of PNNT-BZCF composite ceramics (a) x=0.9; (b) x=0.5; (c) x=0.1
3.2 The ferromagnetic hysteresis loop
The magnetic hysteresis loop is the best experimental proof for the ferromagnetic nature of
materials. Up to now, none of ferroelectric ceramics exhibits ferromagnetic character at
room temperature, so the ferromagnetic behaviors of composite ceramics are dominated by
the ferrite phase. For the application in high frequency, soft magnetic material is needed for
the composite materials.
The magnetic hysteresis loops of PNNT-BZCF composite ceramics is plotted in Fig. 8. The
ferromagnetic characters of composite ceramics are only inherited from those of the
magnetic phase of Y-type hexagonal ferrite, so all the samples exhibit soft magnetic
character with low coercive force H
c
and low remnant magnetization M
r
. The coexistence of
magnetic hysteresis loop and P-E loop implies that the PNNT-BZCF composite ceramics
have both ferromagnetic and ferroelectric properties at room temperature, which also
confirms the possibility to achieve both high permittivity and permeability.
Fig. 9 shows the composition dependence of M
s
, M
r
and H
c
for PNNT-BZCF composite
ceramics before and after sintering process. For the green sample before sintering, M
s
and
M
r
both decrease monotonously with the reduction of BZCF amount, while H
c
keeps a
constant. The magnetic properties of green samples are dominated by the nature of
individual magnetic particles and there is little interaction between constituent phases due
to loose microstructure. The linear decrease of M
s
and M
r
is only a result of dilution effect.
The small ferrite particles and lots of defects in microstructure endow the green samples a
relatively high H
c
, which is insensitive to the variation of composition.
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and High Permeability in Hyper-Frequency

195

Fig. 8. The magnetic hysteresis loops of PNNT-BZCF composite ceramics

Fig. 9. The composition dependence of (a) M
s
, (b) M
r
and (c) H
c
for the composite ceramics
of PNNT-BZCF before (□) and after (■) sintering process
After the sintering process, M
s
decreases monotonously with the reduction of ferrite amount
if the mechanical interaction between two constituent phases is weak. For example, M
s

varies near linearly with the ferrite content in BaTiO
3
-NiCuZn ferrite or PMNZT-NiCuZn
ferrite composite ceramics, where ferroelectric phase and ferrite phases are both of equiaxial
grains and little internal stress is produced after co-firing process (Qi et al., 2004).
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196
If the microstructure varies notable after co-firing process, the magnetic properties of
composite ceramics will be affected (Bai et al., 2009). With the reduction of BZCF amount in
PNNT-BZCF composite materials, M
s
, M
r
and H
c
of the sintered samples increase first, reach
a maximum at x=0.3, and then decrease (Fig. 9). The enhancement of M
s
in the range of
0.1<x<0.3 originates from the internal stress produced in the co-firing process. It is reported
that the structural distortion can generate spontaneous magnetization in several composite
materials (Kanai et al., 2001 & Kumar et al., 1998). In PNNT-BZCF composite ceramics, the
enhancement of M
s
in the range of 0.1<x<0.3 is also thought as a result of the internal stress
induced structural distortion, which has been detected by XRD spectra and SEM images. A
more notable enhancement of M
r
and H
c
is observed in the range of 0.1<x<0.3, because M
r

and H
c
are more sensitive to the microstructure. The stress on ferrite grains increases the
resistance of domain wall‘s motion and spin rotation, so the magnetization reversal under
external magnetic field becomes more difficult, which is reflected as the increase of M
r
and
H
c
. When ferrite’s amount decreases further, the dilution effect dominates the magnetic
properties of composite ceramics, and then M
s
, M
r
and H
c
decline monotonically.

Fig. 10. Frequency dependence of permittivity of PNNT-BZCF composite ceramics
4. The permittivity and permeability in hyper-frequency
4.1 Permittivity
Owing to the polarization of dipolar, ferroelectric ceramics always have significant
permittivity higher than several thousands, while the permittivity of ferrite may be as low as
~20. The dielectric mechanism of ferrite is associated with the conduction mechanism, which
is attributed to the easy electron transfer between Fe
2+
and Fe
3+
. Although some ferrite
containing large amount of Fe
2+
ions has high permittivity of several thousands, such as
MnZn ferrite, the low electric resistivity limits its application in high frequency. When the
sintering temperature is lower than 1100
o
C or the sample is sintered under high partial
pressure of oxygen, the sample has high resistivity and low permittivity of ~20, which is
suitable for the application in high frequency.
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197
The permittivity of two-phased composite material is always between those of two
constituent phases and controlled by their relative volume fractions. Since the permittivity
of ferroelectric ceramics is much higher than that of ferrite, the composite ceramics with
more ferroelectric phase have higher permittivity. Fig. 10 shows the frequency dispersion of
permittivity of PNNT-BZCF composite ceramics. The permittivity increases monotonically
with the rise of PNNT amount. For example, the permittivity increases from 30 to 6600 (@
10MHz) when the weight fraction of PNNT rises from 0.1 to 0.8.
4.2 Permeability
The permeability of nonmagnetic ferroelectric ceramics is always one, while the soft
magnetic ferrites have high permeability. Due to the inverse proportion of permeability and
cut-off frequency, the permeability turns lower in higher frequency range, which is
associated with the magnetic structure of material. For example, the permeability of NiZn
and MnZn spinel ferrites is higher than several thousands below MHz frequency range, but
it turns very low above MHz, that is attributed to their cubic structure. The hexagonal
ferrites, especially Y-type hexagonal ferrite, have planar magnetocrystalline anisotropy,
which endows them high permeability above 100MHz. Because the ferrite has much higher
permeability than ferroelectric ceramics, the permeability of composite ceramics increases
with the rise of ferrite’s amount (Fig. 11).

Fig. 11. Frequency dependence of real part and imaginary part of complex permeability of
the composite ceramics of PNNT-BZCF (x=0.1~0.8)
4.3 The theoretical prediction
The effective macroscopic electromagnetic properties of a composite material are
determined by the intrinsic characters of constituent phases and their relative volume
fractions, so some mixture theories and equations have been established based on an
equivalent dipole representation to predict the electromagnetic properties of a composite
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198
material. In this section, three most popular mixture theories are introduced, including
mixture law, Maxwell-Garnett equations (containing MGa, MGb) and Bruggeman effective
medium theory (EMT).
The mixture law is the simplest mixture theory to predict the properties of a composite
material. According to the structure type of a composite material, the mixture law has
different forms, such as parallel connection model and series connection model. For the
composite material with powder mixture, the mixture law has a form as

*
ln ln ln
a a b b
f f Ψ = Ψ + Ψ (1)
where Ψ
*
, Ψ
a
and Ψ
b
are the effective dielectric permittivity or magnetic permeability of
composite material and two constituent phases. The
a
f and
b
f refer to the volume fraction
of two phases and
a
f +
b
f =1.
Further, some mixture theories are developed based on an equivalent dipole representation
of the mixture, where the effective macroscopic electromagnetic properties of composite
material are modeled as the intrinsic dipole moments per unit volume of each constituent
phase and the relative volume fraction. It is assume that the isolated particles of constituent
phases are embedded in a matrix host. The electric and magnetic intrinsic dipole moments
of component phases, as well those of matrix host, are used to calculate the effective
macroscopic properties of composite material. In static (or quasistatic) regime, a general
form of the mixture equation was established based on the assumption that the components
of isolated particles are embedded in a contiguous host medium (Aspnes, 1982). It can be
expressed as

*
*
2 2
b a b
a
b a b
f
Ψ − Ψ Ψ − Ψ
=
Ψ + Ψ Ψ + Ψ
(4)
Different values of Ψ
*
can be calculated using MGa and MGb equations for a composite
material with a given volume fraction of particles. It is because the properties of matrix host
are dominated until the volume fraction of isolated particle closely approaches unity. This
expression works fairly well provided the inclusions make up a small fraction of the total
volume. However, the Maxwell-Garnett model omits the variation of microstructure, so the
imbedded phase never percolates even when the matrix has obviously inverted.
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and High Permeability in Hyper-Frequency

199
To characterize the microstructural inversion, Bruggeman effective medium theory is
formed (Bruggeman, 1935), where the host material is chosen as the mixture itself (Ψ
*
=Ψ
h
),
and then Equation (2) is reduced as
0
2 2
a h b h
a b
a h b h
f f
Ψ − Ψ Ψ − Ψ
= +
Ψ + Ψ Ψ + Ψ
(5)
Bruggeman effective medium theory assumes that component a and b are both embedded
in the effective medium itself and are not treated as contiguous constituents, so it can
predict percolation of either phase when its volume fraction is over 1/3. Its predictions
exhibit a significant improvement compared with MG equations. This formalism has more
applicability for composites formed by the constituents with similar mechanical properties.
In this section, component a and b are chosen as ferroelectric ceramics and ferrite,
respectively. To exclude the influence of frequency dispersion, the experimental data of
permittivity or permeability are accessed in region where the value is steady within a wide
frequency range.
Fig. 12 compared the measured permittivity and calculated values by different equations for
PNNT-BZCF composite ceramics. Mixture law and MGa equation give good predictions of
permittivity for the composite ceramics with less ferroelectric phase, while the calculated
results greatly deviates from the experimental data if PNNT’s amount is large. On the
contrary, MGb equation works well only if PNNT’s amount is very high. EMT result
matches the experimental data well if one phase has much higher volume fraction than the
other, but it does not work well when two phases have comparable volume fraction. In
addition, MGa and MGb equations offer upper and lower limits for the permittivity of
PNNT-BZCF composite ceramics.

Fig. 12. The composition dependence of measured and calculated permittivity of PNNT-
BZCF composite ceramics
The theoretical predicted permeability and experimental data of PNNT-BZCF composite
ceramics are shown in Fig. 13. The prediction by MGa equation fits the experimental data
well over the whole range of compositions, while those of other equations are higher than
the measured data.
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200

Fig. 13. The composition dependence of measured and calculated permeability of the
composite ceramics of PNNT-BZCF

Fig. 14. The composition dependence of measured and calculated permeability of the
composite ceramics of PNNT-NiCuZn ferrite
To further check the applicability of these mixture theories for permeability, the composite
ceramics of PNNT-NiCuZn ferrite is discussed, where NiCuZn ferrite has a high
permeability of ~950 (Shen et al., 2005). Fig. 14 compared the measured permeability and the
values calculated by different equations. The permeability predicted by mixture law, MGa
and EMT equations matches the experimental data well when the ferrite amount is
relatively low. For the composite material with high volume fraction of magnetic phase, all
the equations can not give precise predictions. Although an exact prediction is not
presented, the MGa and MGb predictions give the upper and lower limits to the
permeability of composition material.
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201
The mixture equation based on a single simple model of microstructure may be inadequate
to predict the effective macroscopic dielectric or magnetic properties over the whole
composition range, so more complex equations with two or more models will be used to
achieve wider applicability and more precise prediction.
5. The electromagnetic resonance character in hyper-frequency
5.1 The dielectric resonance
The frequency dispersion character is as important as the values of permittivity and
permeability for the application in high frequency range. Different dispersion characters are
needed by different applications. For example, capacitor or inductor requires a stable
permittivity or permeability and low loss in a certain frequency range, so the resonance
limits its working frequency range; while filter or EMI component needs high loss around
the dielectric or magnetic resonance frequency. In a composite material, the frequency
dispersion is determined by the intrinsic properties of constituent phases and affected by the
interaction between them.

Fig. 15. Frequency dispersion of (a) real part and (b) imaginary part of permittivity of
PNNT-BZCF composite ceramics
The frequency dispersion of real part and imaginary part of permittivity of PNNT-BZCF
composite ceramics is shown in Fig. 15 (a) and (b). A strong dielectric resonance peak is
observed above 100MHz, which originates from the dipole’s vibration (Bai et al., 2006) or
the followed piezoelectric vibration (Ciomaga et al., 2010). The resonance frequency
increases with the reduction of PNNT amount and shifts out of the upper limit of
measurement when the weight fraction of PNNT is lower than 0.4 (Fig. 16). In addition, the
resonance peak turns flatter with the reduction of PNNT amount, which is characterized as
the variation of half peak breadth in Fig. 17. The change of the shape of resonance peak
implies that the dielectric response tends to transform from resonance to relaxation.
In addition to the intrinsic properties of constituent phases, the electromagnetic interaction
between ferroelectric and ferromagnetic phases influences the frequency and shape of
resonance peak. The charged particles in ferroelectric phase vibrate under the force of
external electric field. When the frequency of alternating electric field matches the nature
frequency of the charged particles’ vibration, dielectric resonance occurs. In the ferroelectric-
ferromagnetic composite material, the spatial inhomogeneous electromagnetic field around
ferrite grains will disturb the charged particles’ motion in ferroelectric phase and change
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202
their nature frequency. The equivalent damping for the charged particles’ motion increases
with the enhancement of magnetic phase, so the dielectric response changes from resonance
to relaxation gradually. Since the macroscopic frequency spectra of permittivity reflects the
statistical average effect of microscale charged particles, the resonance peak turns flatter and
shifts to higher frequency with the rise of ferrite amount.

Fig. 17. The composition dependence of the half peak breadth of dielectric resonance peak
for PNNT-BZCF and PNNT-BCCF composite ceramics
The electromagnetic interaction between two phases is affected by the permeability of
magnetic phase. Fig. 17 (a) compares the dielectric dispersions of PNNT-BZCF and PNNT-
Ba
2
Co
1.2
Cu
0.8
Fe
12
O
22
(BCCF) composite ceramics with same composition ratio, where BZCF
and BCCF have identical properties in sintering character, microstructure, permittivity, and
electric resistivity, except for in permeability. The permeability of BZCF (>20) is much
higher than that of BCCF (~3.5). From Fig. 18, two composite materials have same dielectric
The Ferroelectric-Ferromagnetic Composite Ceramics with High Permittivity
and High Permeability in Hyper-Frequency

203
behavior of permittivity except for the distinctly different resonance characters. The
dielectric resonance peak of PNNT-BCCF composite ceramics is narrow and sharp, while
that of PNNT-BZCF composite ceramics is much wider and smoother. The comparison of
half peak breadth shows the contrast in Fig. 17. The induced magnetic field around ferrite
particles is enhanced with the permeability of ferrite, but the variation of electromagnetic
environment is not strong enough to change the value of permittivity within low frequency
range and can only vary the resonance character, which is sensitive to surrounding
condition.

Fig. 18. The comparison of the dielectric frequency spectra of PNNT-BZCF and PNNT-BCCF
composite ceramics

Fig. 19. Frequency spectrum of permeability of BZCF and the divided contributions of
domain wall motion and spin rotation
5.2 The magnetic resonance
The frequency dispersion of permeability of ferroelectric-ferromagnetic composite ceramics
is determined by the nature of magnetic phase. In the frequency spectra of a soft magnetic
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204
ferrite, there will be some kinds of resonances, such as magnetic domain wall resonance and
spin resonance. As shown in Fig. 19, there are two resonance peaks in the frequency spectra
of permeability, where the low-frequency peak originates from the domain wall resonance
and the high-frequency peak results from the spin resonance (Bai et al., 2004). The
permeability can be divided into two parts according to the contributions of domain wall
motion and spin rotation, μ
total
= μ
domain
+ μ
spin
, as shown in Fig. 19.
For the composite ceramics with high ferrite fraction, there are still two resonance peaks in
the frequency spectra (Fig. 19). With the reduction of BZCF amount, the permeability
decreases, and the resonance peaks turn flatter and weaker gradually on account of dilution
effect.

Fig. 20. Frequency dispersion of (a) real part and (b) imaginary part of complex permeability
of PNNT-BZCF composite ceramics
The frequency dispersion of composite ceramics’ permeability is influenced by the
microstructure, such as internal stress. For the samples with large BZCF amount (x<0.3), two
resonance peaks appear in the frequency spectra of permeability. Spin rotation is much
sensitive to the internal stress on magnetic particles, so the spin resonance peak disappears
when x>0.2. In contrast, the domain wall resonance peak exists up to x=0.7.
6. Summary
With the rapid development of electronic products, the multi-functional ferroelectric–
ferromagnetic composite materials are great desired by various novel electronic components
and devices. Then various composite systems and preparation methods were widely
investigated and encouraging progresses have been made. To avoid co-firing mismatch and
achieve a fine microstructure, the materials with similar densification behavior are desired
as the constituent phases in the composite ceramics. And low sintering temperature is
needed not only by the technical requirement of LTCC but also to avoid the element
diffusion, volatilization and formation of other phase.
To keep up with the trend towards higher frequency for electronic technology, the
composite materials with both high permittivity and permeability in hyper frequency is
developed in recent years. The co-fired composite ceramics of 0.8Pb(Ni
1/3
Nb
2/3
)O
3
-
0.2PbTiO
3
/Ba
2
Zn
1.2
Cu
0.8
Fe
12
O
22
are mainly introduced in this chapter, which has excellent
co-firing behavior, dense microstructure and good electromagnetic properties. Owing the
intrinsic characters of constituent phases, the composite ceramics exhibit both ferromagnetic
The Ferroelectric-Ferromagnetic Composite Ceramics with High Permittivity
and High Permeability in Hyper-Frequency

°C for 0.5 h in air. In order to remove the historical effect, all the as-prepared
samples were deaged by holding them at 500 °C for 1 h followed by an air-quench to room
temperature. The quenched and deaged samples are designated as “fresh samples”. Some
fresh samples were aged at 130 °C for 5 days, and the resulting samples are denoted as
“aged samples”.
2.2 Property measurements
The temperature dependence of dielectric constant of the fresh samples was evaluated at
different frequencies using a LCR meter (HIOKI 3532) with a temperature chamber. The
bipolar and unipolar ferroelectric hysteresis (P–E) loops and electrostrain (S-E) curves for
the aged and fresh samples were measured at a frequency of 5 Hz using a precision
ferroelectric test system (Radiant Workstation) and a photonic displacement sensor (MTI
2000) under various temperatures in a temperature-controlled silicon oil bath (Fig. 2).

Fig. 3. Temperature dependence of dielectric constant for the fresh samples at three different
frequencies of 0.1, 1, and 10 kHz. C=cubic, T=tetragonal, O=orthorhombic, and
R=rhombohedral
3.2 Room-temperature bipolar and unipolar ferroelectric hysteresis loops and
electrostrain curves
Fig. 4 illustrates the bipolar and unipolar ferroelectric hysteresis (P–E) loops and
electrostrain (S-E) curves for the aged and fresh samples at room temperature. In contrast
with the normal bipolar P–E loop for the fresh samples, the aged samples in Fig. 4(a) possess
an interesting bipolar double P–E loop, very similar to that of the aged acceptor-doped
tetragonal ferroelectrics such as the A
2+
B
4+
O
3
system (Ren, 2004; Zhang & Ren, 2005; Zhang
& Ren, 2006). Moreover, a large recoverable electrostrain of 0.15% at 5 kV/mm,
accompanying the double P–E loop, is achieved in our aged samples. This recoverable S–E
curve is indeed different from the butterfly irrecoverable S–E curve as obtained in the fresh
samples due to the existence of a recoverable domain switching in the aged samples but an
irrecoverable domain switching in the fresh samples. Fig. 4(b) shows the unipolar P–E loops
and S–E curves for the aged and fresh samples. It is clear that a large polarization P of about
22 μC/cm
2
is obtained at 5 kV/mm for the aged samples compared to a much smaller P of
about 6 μC/cm
2
in the fresh samples at the same field level. With the large P, a large
nonlinear electrostrain of 0.15% at 5 kV/mm is available for the aged samples owing to the
reversible domain switching. It is noted that this electrostrain not only is 2.5 times larger
than the fresh samples, but also exceeds the “hard” lead zirconate titanate (PZT) value of
0.125% at 5 kV/mm (Park & Shrout, 1997). It is also noted that the electrostrain in our fresh
Aging-Induced, Defect-Mediated Double Ferroelectric Hysteresis Loops and Large Recoverable
Electrostrain Curves in Mn-Doped Orthorhombic KNbO
3
-Based Lead-Free Ceramics

211
samples (having a small quantity of Mn acceptor dopant) is not obviously different from
that in the undoped K(Nb
0.90
Ta
0.10
)O
3
ceramic, and similarly large electrostrain has been
reported recently on the aged tetragonal K(Nb
0.65
Ta
0.35
)O
3
-based ceramics (Feng & Ren,
2007).

the single-crystal grain of the fresh samples shows a tetragonal crystal
symmetry 4mm, due to the displacement of positive and negative ions along the [001]
crystallographic axis, producing a nonzero spontaneous polarization P
S
as shown in Fig.
5(b). However, the short-range ordering (SRO) distribution of point defects keeps the
same cubic defect symmetry m3m as that in the cubic paraelectric phase because the
diffusionless paraferroelectric transition cannot alter the original cubic SRO symmetry
of point defects (Ren, 2004).
3. At T
R-O
<T<T
O-T
,

213
crystallographic axis as shown in Fig. 5(c). Again, the SRO distribution of point defects
still keeps the same cubic defect symmetry m3m because of fast cooling. As a result, two
unmatched symmetries (i.e., the orthorhombic crystal symmetry and the cubic defect
symmetry) exist simultaneously in the fresh ferroelectric state

[Fig. 5(c)]. According to
the SC-SRO principle (Ren & Otsuka, 2000), such a state is energetically unstable and
the samples tend to a symmetry-conforming state.
4. After aging at 130 °C for 5 days in the ferroelectric state, the cubic defect symmetry m3m
changes gradually into a polar orthorhombic defect symmetry mm2, while the single-
crystal grain of the aged samples has a polar orthorhombic crystal symmetry mm2, as
shown in Fig. 5(d). Such a change is realized by the migration of V
O
during aging, and
the polar orthorhombic defect symmetry creates a defect polarization P
D
, aligning along
the spontaneous polarization P
S
direction [Fig. 5(d)].
5. When an electric field E is initially applied in opposition to P
S
of the aged orthorhombic
samples [Fig. 5(e)], an effective switching of the available 180° ferroelectric domains is
induced, contributing to a small polarization at low E (<1.5 kV/mm), as shown in Fig.
4(b). Continuing a larger applied E (>1.5 kV/mm), non-180° domain switching (mainly
60° and 120° domain switching according to the polar orthorhombic crystal symmetry)
is induced, but the polar orthorhombic defect symmetry and the associated P
D
cannot
have a sudden change [Fig. 5(e)]. Hence, the unchanged defect symmetry and the
associated P
D
cause a reversible domain switching after removing E. Consequently, an
interesting macroscopic double P–E loop and a large recoverable S–E curve are
produced as in Fig. 4. For the fresh samples, since the defect symmetry is a cubic
symmetry and cannot provide such an intrinsic restoring force, we can only observe a
normal macroscopic P–E loop and a butterfly S–E curve due to the irreversible domain
switching [Fig. 4(a)].
It should be noted that the microscopic description for the orthorhombic KNbO
3
-based
ferroelectrics is very similar to that for acceptor-doped tetragonal ferroelectric titanates (Ren,
2004; Zhang & Ren, 2005; Zhang & Ren, 2006). The observed aging effects originate
essentially from the inconformity of the crystal symmetry with the defect symmetry after a
structural transition. This may be the intrinsic reason why macroscopic double P-E loops
and recoverable S–E curves are achieved in different ferroelectric phases and different
ferroelectrics. Such aging mechanism, based on the SC-SRO principle of point defects, is
insensitive to crystal symmetry and constituent ionic species, indicating a common physical
origin of aging.
3.4 Effect of temperature on ferroelectric hysteresis loops and electrostrain curves
Fig. 6 plots the unipolar ferroelectric hysteresis (P–E) loops and electrostrain (S–E) curves for
the aged samples at five different temperatures of 25, 80, 120, 140, and 160 °C in order to
investigate their temperature stabilities for applications. The insets show the temperature
dependence of maximum polarization P
max
and maximum strain S
max
of the aged samples at
5 kV/mm. It can be seen that the aging-induced high P
max
in excess of 19 μC/cm
2
and large
S
max
in excess of 0.13% can be persisted up to 140

°C, reflecting a good temperature stability
for the effects. Above 140

°C, both the unipolar P–E loop and S–E curve become normal,
while P
max
and S
max
decrease significantly. This can be ascribed to the destruction of defect
symmetry and migration of V
O
as a result of the exposure to high temperature and the
approach of the tetragonal phase (T
O-T
=148 °C). Thus, point defects cannot provide a
Ferroelectrics

214
restoring force for a reversible domain switching so that the obvious P–E loop becomes a
normal loop and the recoverable S–E curve vanishes.

218
been found, but the properties obtained by the formation of the MPB are still inferior to
those of PZT.
In improving the properties of solid solutions, the characteristics of end members should
be thoroughly evaluated to understand the composition-dependent responses of solid
solutions. However, there have been only a few reports on end member compounds; most
of the studies have attempted to improve important material properties. The basic
properties of BNT are not completely understood; unclear aspects remain. Regarding the
understanding of BNT, there are reports on A-site modifications (Sung et al., 2010; Zuo et
al., 2008; Kimura et al., 2005; Nagata et al., 2005), but there are only a few on B-site
doping.
In this work, the effects of B-site doping in BNT

ceramics were studied using a donor Nb
5+

and an acceptor Mn
3+
for B-site Ti
4+
. Two key properties, dielectric depolarization
temperature (T
d
) and piezoelectric coefficient (d
33
), were evaluated in relation to
microstructure and phase purity. Then, they were compared with donor and acceptor effects
in PZT (Jaffe et al., 1971; Zhang et al., 2008; Erhart et al., 2007; Zhang & Whatmore, 2003;
Randall et al., 1998; Park & Chadi, 1998; Gerson, 1960) to identify similarities and differences
between BNT and PZT ceramics. In addition, the electrical conductivity of BNT was
measured and discussed as a function of the oxygen partial pressure and temperature.
2. Experimental
Powders of at least 3 N purity Bi
2
O
3
(99.9%), Na
2
CO
3
(99.95%), TiO
2
(99.9+%), Nb
2
O
5
(99.9%),
and Mn
2
O
3
(99.999%) were used to prepare (Bi
0.5
Na
0.5
)(Ti
1-x
D
x
)O
3
(D = Nb, Mn) ceramics
through solid-state processing. In handling the raw powders, hygroscopic Na
2
CO
3
was
thoroughly dried in a dry-oven until no change in weight occurred. Then it was quickly
weighed in air; if not, it absorbs moisture from the air and increases in weight, thus
comprising an incorrect composition from the beginning.
The compositions of the samples were controlled to be x = 0–1 mol % for Nb doping and 0–2
mol % for Mn doping. The powders of each composition were ball-milled using yttria-
stabilized zirconia balls and anhydrous ethanol to keep the powders from water. After
milling, powders were dried and calcined twice at 780 °C and 800 °C for 2 h in air to prevent
the premature loss of any component during calcination and to have homogeneous powders
after calcination. Next, they were mixed with 5 wt% polyvinyl alcohol (PVA) aqueous
solution to 0.5 wt% and screened using a 150 µm sieve for pelletizing. Pellets of 10 or 18 mm
in diameter and ~1 mm in thickness were made by uniaxial pressing at 150 MPa. Then, all
the samples were sintered at 1150 °C for 2 h in air. During sintering, the heating rate was
controlled to burn out the PVA at around 500 °C.
The Archimedes principle was applied to estimate the apparent densities of the sintered
pellets, and these values were compared with the theoretical densities. X-ray diffraction
(XRD) patterns generated by a diffractometer with Cu Kα radiation (λ = 1.541838 Å) at 40 kV
and 30 mA were taken from the polished surfaces of sintered pellets and analyzed for
identifying phases. Scanning electron microscopy (SEM) with energy dispersive
spectroscopy was used to detect any secondary phase formation as well as to examine grain
morphology that occurred during sintering.
To measure their properties, the samples were polished on both sides down to 0.5 mm in
thickness using #400, 800, and 1200 emery papers. They were painted with Ag paste and
then cured at 650 °C for 0.5 h in air. Poling of samples was carried out at a dc field of 40
Effects of B-site Donor and Acceptor Doping in Pb-free (Bi
0.5
Na
0.5
)TiO
3
Ceramics

219
kV/cm for 0.5 h in silicone oil at room temperature using a high voltage supply (Keithley
248), and leakage current was monitored using an electrometer (Keithley 6514).
After aging for 24 h, the room temperature d
33
was measured using a piezo d
33
meter (ZJ-6B,
IACAS) at 0.25 N and 110 Hz. The dielectric constant (ε) and the loss tangent (tan δ) at
various frequencies on heating and cooling were measured using an impedance analyzer
(HP4192A). The planar electromechanical coupling factors (k
p
) and mechanical quality
factors (Q
m
) of the samples were calculated from the resonance frequencies (f
r
), the
antiresonance frequencies (f
a
), the resonant impedances (Z
r
), and the capacitances (C
p
) at 1
kHz, measured using an impedance gain phase analyzer (HP4194A). Electric field
dependent polarization (P-E) hysteresis loops were measured using a Sawyer-Tower circuit
to measure remnant polarization (P
r
) and coercive field (E
c
).
3. Results
The weight losses of the samples that occurred during sintering were consistently less than 1
wt%. This was thought to primarily result from the evaporation of moisture, the PVA, and
possibly some of the Bi and Na oxides. The relative apparent densities of the pellets after
sintering were all above ~95% of the theoretical density, indicating that the samples were
consistently prepared under the processing conditions used in this work.
3.1 Phase and microstructure
Figure 1 shows the XRD patterns of (Bi
0.5
Na
0.5
)(Ti
1-x
D
x
)O
3
ceramics with D = Nb or Mn
substituting for Ti in BNT. In the case of a donor Nb doping, no secondary peak was
observed up to 1 mol %, and all the peaks were indexed to be rhombohedral. In the case of
an acceptor Mn doping, XRD patterns were also phase-pure up to 2 mol %.
Fig. 1. XRD patterns of (Bi
0.5
Na
0.5
)(Ti
1-x
D
x
)O
3
ceramics (D = Nb, Mn) sintered at 1150 °C for 2
h in air. Si peaks are of 5 N silicone powder used as an internal standard for calibration
The phase purity of the sintered (Bi
0.5
Na
0.5
)(Ti
1-x
D
x
)O
3
with D = Nb or Mn pellets was
confirmed by SEM images. No secondary phase was observed, as shown in Fig. 2.
Regarding the grain morphology, the grain shapes in general were well developed in both
20 30 40 50 60
2.0 Mn
1.5 Mn
1.0 Mn
0.5 Mn
2
0
1
- -
1
1
1
Si
Si
0.2 Nb
0.4 Nb
0.6 Nb
0.8 Nb
1.0 Nb
BNT
Si
2
1
1
2
1
0
2
0
0
1
1
1
1
1
0
1
0
0

I
n
t
e
n
s
i
t
y

(
a
r
b
.

u
n
i
t
)
2θ (degree)
2
1
1
-
-
1
0
1
-
Ferroelectrics

220
Nb and Mn doping, indicating that the sintering condition was consistent for both donor-
and acceptor-doped samples.

Fig. 2. SEM secondary electron images of the surfaces of (Bi
0.5
Na
0.5
)(Ti
1-x
D
x
)O
3
pellets (D =
Nb, Mn) sintered at 1150 °C for 2 h in air
An obvious difference observed among the images is the grain size relative to doping; the
grain size decreased with Nb doping and increased with Mn doping, depending on the
amount of Nb and Mn doping. The decrease in grain size in the case of Nb donor doping
can be explained by A-site cation vacancies created by B-site donor doping required to
maintain charge neutrality in the lattice. These cation vacancies exist along grain boundaries
rather than inside grains, which is thermodynamically more stable. Grain boundaries would
be pinned by these defects, inhibiting grain growth and resulting in relatively small grains
in the case of donor doping (Yi et al., 2002; Lewis et al., 1985; Lucuta et al., 1985). Mn
acceptor doping, on the other hand, induces oxygen vacancies instead of A-site vacancies
required to maintain charge neutrality in the lattice. It appears that grain growth was not
inhibited by Mn doping inducing oxygen vacancies, as shown in Fig. 2. These different roles
of donor and acceptor that were observed in the microstructure affected the properties of
BNT in different ways.
3.2 Piezoelectric properties
For various piezoelectric applications, d
33
, k
p
, and Q
m
are key properties that need to be
evaluated. As shown in Fig. 3, d
33
gradually increased with Nb donor doping and gradually
decreased with Mn acceptor doping. As mentioned above, B-site donor doping induces A-
Effects of B-site Donor and Acceptor Doping in Pb-free (Bi
0.5
Na
0.5
)TiO
3
Ceramics

222
B-site acceptor doping, on the other hand, reduces A-site vacancy or induces oxygen
vacancy to maintain charge neutrality in the lattice. Acceptor doping produces the results
that are opposite to those produced by donor doping, as shown in Fig. 3. Oxygen vacancy is
relatively mobile; this pins domain walls (Zhang & Whatmore, 2003; Park & Chadi, 1998),
resulting in a lower d
33
unless the vacancy becomes immobile by forming defect complexes
with other defects (Hu et al., 2008; Zhang et al., 2008; Erhart et al. 2007). The increase from
donor doping and the decrease from acceptor doping in the d
33
of BNT ceramics are
generally consistent with the variations from doping in the d
33
of PZT-based ceramics (Jaffe
et al., 1971). Regarding the microstructure, d
33
appears to be inversely related to grain size.
The trend observed in k
p
, as shown in Fig. 4, was similar to that observed in d
33
. A slight
increase from Nb donor doping and a gradual decrease from Mn acceptor doping occurred;
this is consistent with the typical outcomes of B-site donor and acceptor doping in PZT.
Fig. 5. Mechanical quality factor (Q
m
) of (Bi
0.5
Na
0.5
)(Ti
1-x
D
x
)O
3
ceramics (D = Nb, Mn)
Q
m
, on the contrary, decreased with Nb donor doping and increased with Mn acceptor
doping, as shown in Fig. 5. Regarding mechanical loss, it is expected that the grain
boundary would cause more loss than the grain itself. As grain size increases, grain
boundary area decreases, yielding a higher Q
m
. This result can be coupled with the variation
in grain size according to doping, as shown in Fig. 2. Q
m
became smaller as grain size
became smaller with Nb donor doping, but it became slightly larger as grain size became
slightly larger with Mn acceptor doping.
3.3 Dielectric properties
For measuring dielectric properties according to changes in doping, the samples were pre-
poled to expose T
d
, as indicated by the arrow marks in Fig. 6. With Nb donor doping both
room temperature ε and tan δ increased while with Mn acceptor doping, ε did not change
significantly and tan δ decreased, as shown in Fig. 6. These dielectric results of BNT with B-
site donor and acceptor doping are similar to those of PZT with doping, although the two
are dielectrically different materials.
0.0 0.5 1.0 1.5 2.0
100
200
300
400
500

225
In the experimental results, the dlogσ/dlogpO
2
slopes are clearly negative in the temperature
range tested. Therefore, the conduction behavior of BNT can be considered as n-type in the
elevated temperature range.
3.5 Other properties
In addition to the above-mentioned piezoelectric and dielectric properties, other properties,
such as ferroelectric and electrical properties, must be considered in relation to practical
applications. For instance, E
c
, P
r
, and leakage current density (J
leak
) are important properties
that need to be characterized. Table 1 summarizes certain properties measured with various
B-site donors and acceptors.
As shown in Table 1, with donor doping, E
c
decreased and P
r
increased. Similar results were
obtained regardless of the donor material (Nb
5+
, Ta
5+
, or W
6+
). With acceptor doping, on the
other hand, E
c
increased and P
r
decreased. Overall, there were consistent trends in the case
of donors, but the results with acceptors were not as consistent as those with donors.
Regarding J
leak
at room temperature, there were some difficulties in taking the
measurement; J
leak
was very low at zero field and was only ~10
-8
A/cm
2
at a dc poling field
of 40 kV/cm. There were no consistent and reliable data values in the literature to compare
because of differences among samples that were caused by different sample preparation
methods.

226
donor and acceptor doping observed in BNT ceramics are similar to those observed in PZT,
but there are also some differences.
For ABO
3
perovskite, as mentioned above, B-site donor doping induces A-site vacancies
while acceptor doping reduces A-site vacancies and induces oxygen vacancies to maintain
charge neutrality in the lattice. A-site vacancies facilitate domain walls motion (Gerson,
1960), which explains a high d
33
and dielectric loss (Jaffe et al, 1971). Oxygen vacancies, on
the other hand, are mobile and pin domain walls; this restricts domain switching, resulting
in a low d
33
and dielectric loss. Oxygen vacancies, however, can be tied up with cation
vacancies forming defect complexes that make them immobile (Hu et al., 2008; Zhang et al.,
2008; Erhart et al. 2007; Zhang & Whatmore, 2003; Park & Chadi, 1998). If this occurs,
domain walls motion is not hindered but grain growth is hindered by grain boundary
pinning caused by defect complexes (Sung et al., 2010).
Coupling the piezoelectric values with the microstructural variations in Fig. 2, a higher d
33

was obtained from smaller grains with Nb donor doping, and a lower d
33
was obtained from
larger grains with Mn acceptor doping. This implies that, in the case of Nb donor doping,
the domain walls must have been unpinned, leading to a high d
33
, while grain boundaries
must have been pinned, causing small grains. The situation was reversed in the case of Mn
acceptor doping. Domain walls must have been pinned, leading to a low d
33
, while grain
boundaries must have been unpinned, causing large grains. This indicates that oxygen
vacancies, if they were formed by Mn acceptor doping must have been tied up by the
formation of defect complexes.

227
solutions, but it has not been clearly explained, partly because T
d
is a unique transition in
BNT-based ceramics that cannot be explained in terms of the PZT database. Sung et al.
suggested lattice distortion as a common factor that affects the two properties inversely. If
lattice distortion decreases, d
33
increases through better poling by electric field, but T
d

decreases through easier depoling by temperature.
For doping effects in general, all the explanations have been given in terms of A-site and
oxygen-site vacancies. In terms of the ionic sizes, Mn
3+
, Ti
4+
, Nb
5+
, Ta
5+
, and W
6+
(but not
Sc
3+
) are similar, as shown in the comparison with Ti
4+
in Table 1. In cases of similar ionic
size, there will be minimal change in the shape and size of the lattice. With a small amount
of doping, therefore, it would be difficult to detect any variation in the XRD patterns.
Indeed, as shown in Fig. 9, there was no apparent change in peak positions caused by Nb
donor or Mn acceptor doping. It would be interesting to know if any variation in lattice
parameters occurs in the case of a substantial amount of doping with a relatively large
difference in ionic radii.
Fig. 9. Detailed XRD patterns of (Bi
0.5
Na
0.5
)(Ti
1-x
D
x
)O
3
ceramics (D = Nb, Mn), from the
patterns shown in Fig. 1
There are some data regarding donor doping effects in BNT-based ceramics, but little
information is available about acceptor doping effects. This situation could exist because
acceptors with 3+ valence can be on either the B-site Ti or the A-site vacancy, considering
the volatile A-site Bi
3+
and Na
1+
. For dornors with 5+ or 6+, on the other hand, it is unlikely
that they would occupy the A-site vacancy instead of the B-site Ti. Moreover, even if they
did, the resulting outcomes would still be considered as donor doping effects. As shown in
Table 2, among the data on donor effects, consistent trends can be identified. Grain size, Q
m
,
T
d
, and E
c
decreased, while d
33
and P
r
increased. These trends become reversed with
acceptor doping.
Finally, it cannot be emphasized enough that hygroscopic Na
2
CO
3
must be completely dried
before and during weighing. Otherwise, the nominal compositions of the samples will be
39 40 41 42 45 46 47 48 49
2.0 Mn
1.5 Mn
1.0 Mn
0.5 Mn
-
1
1
1
0.2 Nb
0.4 Nb
0.6 Nb
0.8 Nb
1.0 Nb
BNT
Si
2
0
0
1
1
1

I
n
t
e
n
s
i
t
y

(
a
r
b
.

u
n
i
t
)
2θ (degree)
Ferroelectrics

228
incorrect. If the ionic radius of an acceptor with 3+ valence is larger than that of Ti
4+
, doping
of an acceptor with 3+ valence on Na
1+
vacancy, instead of the Ti
4+
site, might occur. In
addition, there is the possibility of an acceptor with 3+ valence substituting for A-site Bi
3+

instead of for B-site Ti
4+
. This appears to explain the inconsistent results and donor-like
effects (see Table 1) that were observed in Sc
3+
, which has a larger ionic radius than the
others do as compared with that of Ti
4+
. To confirm the acceptor effects in BNT, the next
experiment should include the doping of acceptors with 2+ valence and small differences in
ionic radii.
5. Summary
The effects of a B-site donor, Nb
5+
, and an acceptor, Mn
3+
, for Ti
4+
in Pb-free (Bi
0.5
Na
0.5
)(Ti
1-
x
D
x
)O
3
(D = Nb or Mn) ceramics were studied in terms of microstructure and important
properties. Regarding the microstructure, all the samples retained a perovskite structure
with rhombohedral symmetry with both Nb donor and Mn acceptor doping. No secondary
phase was seen up to x = 1.0 mol % of Nb-doped BNT ceramics and x = 2.0 mol % of Mn-
doped BNT ceramics. The grain size, however, decreased with Nb doping and slightly
increased with Mn doping. In addition to producing variation in microstructure, Nb and Mn
yielded opposite piezoelectric and dielectric outcomes. Higher d
33
, lower Q
m
, and smaller
grain size were obtained from Nb doping, while lower d
33
, higher Q
m
, and larger grain size
were obtained from Mn doping. These results indicate a correlation between piezoelectric
properties and grain size. Regarding the dielectric transition, T
d
decreased with Nb doping,
but it decreased slightly then held steady with Mn doping. Overall, the donor effects
observed in BNT ceramics were similar to those observed in PZT ceramics, but acceptor
effects need to be studied further in order to produce consistent data. At elevated
temperatures, BNT exhibited n-type conduction.
6. Acknowledgments
This work was supported by the National Research Foundation of Korea Grant funded by
the Korean Government (2009-0088570) and the Basic Science Research Program through the
National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science
and Technology (2010-0025055). This research was also financially supported by the
Ministry of Education, Science and Technology (MEST) and Korea Institute for
Advancement of Technology (KIAT) through the Human Resource Training Project for
Regional Innovation.
7. References
Cho, J. H.; Yeo, H. G.; Sung, Y. S.; Song, T. K.; & Kim, M. H. (2008). Dielectric and
piezoelectric characteristics of W-doped lead-free (Bi
0.5
Na
0.5
)(Ti
1-x
W
x
)O
3
ceramics.
New Physics: Sae Mulli (The Korean Physical Society) 57, 409-416.
Dai, Y. J.; Zhang, X. W.; Chen, K. P.; (2009). Morphotropic phase boundary and electrical
properties of K
1-x
Na
x
NbO
3
lead-free ceramics. Appl. Phys. Lett., 94, 042905.
Egerton, L. & Dillon, D. M. (1959). Piezoelectric and dielectric properties of ceramics in the
system potassium-sodium niobate. J. Am. Ceram. Soc., 42, 438-442.
Effects of B-site Donor and Acceptor Doping in Pb-free (Bi
0.5
Na
0.5
)TiO
3
Ceramics

2
Department of Physics, University of Puerto Rico, San Juan, PR-00931
1
India
2
USA
1. Introduction
In recent years, there has been a tremendous interest in ferroelectric materials from
perspective of their potential applications in electronic devices such as non-volatile random
access memories (NvRAMs), pyroelectric infrared detectors and optical switches [1-4]. On
account of their read-write speed, non volatility, low operating power and radiation
hardness, NvFRAMs are promising candidates for substituting silicon based electrically
erasable programmable read-only memories (EEPROMs) and flash EEPROMs. The materials
for memory applications are required to possess the following properties: a large remanent
polarization (P
r
), a low coercive field (E
c
) and sufficient fatigue endurance against repetitive
polarization switching etc. [5]. Among ferroelectrics, lead zirconate titanate PbZr
1-x
Ti
x
O
3

(PZT) has been investigated extensively and has been found to be the most promising
material for NvFRAM applications. However, apart from Pb toxicity, PZT suffers from
serious degrading problems such as fatigue, ageing and leakage current that hinder the
usability of this material in devices [6-10]. Among them fatigue is an important reliability
issue for NvRAM devices which is defined as a decrease in switchable polarization with
increasing number of polarization reversals [11].
During the search for an alternate ferroelectric material for these applications, it was found
that bismuth oxide layered structures (BLSFs) originally synthesized by Aurivillius [12] are
the most suitable candidates due to their relatively high Curie temperature (T
c
), low
dielectric dissipation and anisotropic nature originating from their layered structure [13-15].
The Aurivillius family of layered bismuth-oxides encompasses many ferroelectric materials,
a fact which was known since the pioneering work of Smolenskii [16] and Subbarao [17],
more than forty years ago. SrBi
2
Ta
2
O
9
(SBT), which is an n=2 member of the Aurivillius
family of layered compounds, proved to be a versatile material for multifarious
applications. Since Araujo et. al. [18] reported the fatigue-free behavior of SrBi
2
Ta
2
O
9
(SBT),
it has gained importance among Pb-free ferroelectric memory materials [19-28]. Araujo
recognized the inherent advantage of BLSFs over other ferroelectric materials on account of
the fact that the former have intermediate bismuth oxide layers between the ferroelectric
units [29].
Ferroelectrics

232
Bi
3+
O
2-
Ta
5+

Sr
2+

Fig. 1. The crystal structure of SrBi
2
Ta
2
O
9

Fig. 1 depicts the crystal structure of SrBi
2
Ta
2
O
9
consisting of (Bi
2
O
2
)
2+
layers and perovskite-
type (SrTa
2
O
7
)
2-
units with double TaO
6
octahedral layers [30]. Besides improvement in the
fatigue characteristics, a longer polarization retention time, lesser tendency to take an
imprint [30,31], high dielectric constant and low switching fields have also been observed in
SBT [32], which are better than those of PZT [18, 33-34]. The high fatigue endurance to
repetitive switching of polarization (≈10
12
switching cycles) is believed to originate from the
anisotropic nature of SBT. It has been argued that the (Bi
2
O
2
)
2+
layers control the electronic
response [35-36] and perform the primary function in preventing degradation of remanent
charge [35,37]. The ferroelectricity arises mainly in the perovskite blocks [15, 35, 38-40]. The
dielectric constant peak corresponding to a ferro-paraelectric transition has been reported in
the range of 300–320 ˚C [35, 38].Though SBT shows improved ferroelectric properties [41-
42], its piezoelectric properties have not been investigated in detail. Kholkin et. al. [43]
reported on the electromechanical properties of SBT but the maximum piezoelectric
coefficient that was measured was quite small.
Enhanced Dielectric and Ferroelectric Properties of Donor (W
6+
, Eu
3+
)
Substituted SBT Ferroelectric Ceramics

233
In this chapter effect of tungsten and europium substitution on dielectric, conductivity,
piezoelectric and ferroelectric properties of SBT ceramics have been carried out and the
results are presented.
2. Experimental techniques
The polycrystalline SrBi
2
Ta
2
O
9
(SBT) ferroelectric ceramics doped with W (tungsten) and Eu
(europium) having the following compositions were prepared by the solid state reaction
technique:
SrBi
2
(Ta
1-x
W
x
)
2
O
9
; x = 0.0, 0.025, 0.050, 0.075, 0.10, 0.20
Sr
1-x
Eu
x
Bi
2
Ta
2
O
9
; x = 0.0, 0.025, 0.050, 0.10, 0.20
The starting chemicals used were strontium carbonate (SrCO
3
), bismuth oxide (Bi
2
O
3
),
tantalum oxide (Ta
2
O
5
), tungsten oxide (WO
3
) and europium oxide (Eu
2
O
3
). The chemicals
were weighed in stoichiometric proportions as mentioned above. The weighed powders
were mixed and thoroughly ground and passed through sieve of appropriate mesh size. The
ground powder was calcined at 900 ˚C in air for two hours. Thereafter, the calcined powder
was pressed into disk shaped pellets. The pellets were sintered in air at 1200 ˚C. The sintered
pellets were polished to a thickness of nearly 1mm. High temperature conductive silver
paste was used for electroding the parallel surfaces. After applying the silver paste, the
pellets were cured at 550˚C for half an hour before electrical characterization. X-ray
diffractograms of all the samples were recorded for the structural analysis using Bruker X-
ray diffractometer with CuK
α
radiation of wavelength 1.54439 Å in the range from 10˚≤ 2θ
≤70˚ at a scanning rate of 0.05˚ / second. The SEM micrographs of the fractured surfaces of
the samples were obtained using the Cambridge Stereo Scan 360 scanning electron
microscope. A Solartron 1260 Gain-phase impedance analyzer was used for measuring the
dielectric constant and dielectric loss in the present work. The d.c conductivity was
measured using Keithley’s 6517A electrometer. Hysteresis measurements were done at
room temperature using an automatic PE loop tracer based on Sawyer-Tower circuit at
switching frequency of 50 Hz. The piezoelectric coefecient, d
33
was measured using a
Berlincourt d
33
meter.
3. Results and discussion
3.1 XRD analysis
The observed XRD patterns of the studied samples having different concentrations of
tungsten and europium are shown in Fig. 2(a) and (b), respectively. The XRD patterns of the
SrBi
2
(Ta
1-x
W
x
)
2
O
9
samples show the characteristic peaks of SBT. The peaks have been
indexed with the help of a computer program – POWDIN [44] using the observed
interplanar spacing d. It is observed that the single phase layered perovskite structure is
maintained in the range 0.0 ≤ x ≤ 0.05. An unidentified peak of very low intensity is
observed in the composition with x > 0.05. In all the diffraction patterns, peaks shift slightly
towards higher diffraction angle with increasing W concentration implying a decrease in
lattice parameters. This can be understood from the fact that the ionic radius of W
6+
(0.60Å)
is smaller in comparison to Ta
5+
(0.64Å). On the other hand no extra peaks are observed in
Ferroelectrics

234
the XRD patterns of Sr
1-x
Eu
x
Bi
2
Ta
2
O
9
samples. It can therefore be concluded that the single
phase layered perovskite structure is maintained in all the SEBT samples. The calculated
lattice parameters for both the series are tabulated (Table 1).
(b)
(a)

samples
3.2 Morphological studies
Figs. 3 and 4 show the surface morphology of the SBTW and SEBT samples respectively. A
systematic study of the micrographs reveals porous and loosely packed grains for the pure
sample. From the figures one can notice an increase in the average grain size, homogeneity
and relatively packed microstructure with W and Eu substitution. Randomly oriented and
anisotropic plate-like grains are observed in all the W substituted samples. The average
Enhanced Dielectric and Ferroelectric Properties of Donor (W
6+
, Eu
3+
)
Substituted SBT Ferroelectric Ceramics

237
The observed variation in T
c
& peak-
r
ε with concentration is explained in the ensuing
paragraph. Generally in isotropic perovskite ferroelectrics, doping at B-site (located inside
an oxygen octahedron) with smaller ions results in the shift of the Curie point to a higher
temperature, leading to a larger polarization due to the enlarged “rattling space” available
for smaller B-site ions [37]. However, in the anisotropic layered-perovskites, the crystal
structure may not change as freely as that in the isotropic perovskites with doping due to
the structural constraint imposed by the (Bi
2
O
2
)
2+
interlayer [47-48]. On comparing the
variation of in-plane lattice parameters a and b (Table 1) with tungsten concentration, we
observe that with increasing tungsten concentration a decrease in the lattice parameters a
and b is observed. It is this enhancement of ferroelectric structural distortion along with the
introduction of cation vacancies at the A-site that lead to an eventual increase in T
c
value [21,
25, 47, 49-50]. In Fig. 5 (a) it is observed that peak-
r
ε increases with increasing tungsten
concentration. The high T
c
which is indicative of enhanced polarizability [21, 36, 51-52],
explains the increase in peak
r
ε . Moreover, since the valency of the substitutional cation
(W
6+
) is higher than the Ta
5+
, the substitution creates cationic vacancies at Sr-site (
"
Sr
V ) to
maintain electrical neutrality of the lattice structure [22, 47, 53]. In the tungsten doped
samples, because of the constraint of maintaining overall charge neutrality of the structure,
substitution of W
6+
ions for Ta
5+
in the structure result in the formation of cation vacancies at
A-sites. For substitution of two W
6+
ions, one A-site (Sr site) remains vacant. The process can
be represented as:

"
1
2
Ta Sr
Null W V
•
= + (1)
where
Ta
W
•
represents tungsten replacing tantalum site and
"
Sr
V denotes the Sr-vacant site. It
has been reported that cation vacancies make the domain motion easier and increase the
dielectric permittivity [53-54] and thus an increase in
r
ε with increasing W content is
observed. There is also a possibility that the microstructural development due to
compositional deviation from the stoichiometry affect the dielectric properties. It is expected
that the domain walls are quite free in their movement in larger grains than smaller sized
grains, since grain boundaries contribute additional pinning points for the moving walls
[55-56]. Increase in the grain size makes the domain wall motion easier which results in an
increase in the dielectric permittivity [41]. Since the grain size increases with sintering W
concentration (Fig. 3), an increase in peak -
r
ε is observed.
Fig. 5 (b) shows the tangent loss (tanδ) as a function of temperature in W-doped samples
measured at 100 kHz. It is observed that tungsten doping in SBT reduces dielectric loss
significantly. The dissipation in ferroelectric materials occurs due to various causes such as
domain wall relaxation, space charge accumulation at grain boundaries, dipolar losses, dc
conductivity, etc. [45]. The presence of oxygen vacancies
o
V
••
, which act as space charge and
contribute to the electrical polarization can be related to the dielectric loss [50, 57-58]. The
substitution of W
6+
for Ta
5+
in SBT results in the formation of cation vacancies which
effectively reduces the concentration of oxygen vacancies which in turn significantly reduce
the dielectric loss. Reduction in loss have been reported in other donor doped BLSFs also
[25, 49].
Ferroelectrics

238
Fig. 5(c) shows the temperature dependence of dielectric permittivity at 100 kHz for SEBT
samples. The substitution of Eu in SBT lowers and broadens the ferro-paraelectric phase
transition temperature. The broadened peaks, as observed in Fig. 5c, indicate that transition
in all the samples is of diffuse type, an important characteristic of a disordered perovskite
structure [59]. The broad peak implies that the ferroelectric - paraelectric phase transition
does not occur at discrete temperature but over a temperature range [11]. The broadening or
diffuseness of peak occurs mainly due to two mechanisms. One is due to the substitution
disordering in the arrangement of cations at one or more crystallographic sites in the lattice
structure leading to heterogenous domains [60]. Another possible explanation of broadened
peak is due to the defect induced relaxation at high temperature [60-61].
Comprehensive structural analysis of SBT with the aid of neutron diffraction and Raman
scattering have shown disorder in the distribution of the Sr ions and Bi ions [62-63]. Recent
independent studies by Ismunandar et. al. [64] and Blake et. al. [62] have reported that there
is a significant degree of Sr/Bi cation disorder in the SrBi
2
Nb
2
O
9
compounds. Thus, it is
possible that cation disorder between Sr and Bi sites also occurs in the tantalum analogues
[51, 66]. Macquart et. al. [67], provided conclusive evidence of cation disorder in ABi
2
Ta
2
O
9
,
where A = Ca, Ba, Sr. As already mentioned pristine SrBi
2
Ta
2
O
9
is not perfectly
stoichiometric and contains a certain amount of inherent defects (e.g. oxygen vacancies)
resulting from the volatilization of Bi
2
O
3
at high temperatures. When Bi
2
O
3
is lost, bismuth
and oxygen vacancy complexes are formed in the (Bi
2
O
2
)
2+
layers [58, 68]. Hence, such
disorder in the arrangements of cations at A-sites (in perovskite- like unit) and Bi sites (in
Bi
2
O
2
layers) is likely to be present. It is because of the cation disordering, that ions at A and
B site are not homogenously distributed on a microscopic scale. Such compositional
fluctuations lead to a microscopic heterogeneity in the structure that consists of
microdomains having slightly different chemical compositions [69-70]. These microdomains
with different chemical compositions will have different ferro-paraelectric transition
temperatures. This distribution of T
c
induces a gradual ferroelectric transition leading to
broadening of the peak [48, 69-71]. In the context of above discussions, it is highly probable
that some Eu
3+
ions, in addition to occupying Sr
2+
sites, also occupy the available bismuth
vacant sites in the Bi
2
O
2
layer. In other words, there is a possibility of inhomogenous
distribution of Eu ions in perovskite blocks and (Bi
2
O
2
)
2+
layers. This can be expressed as:

'''
Bi Bi
Eu V Eu Null
•••
+ = = (2)
The above expression denotes the occupancy of Eu ion ( Eu
•••
) at the vacant Bi site (
'''
Bi
V );
since Eu has +3 charge and Bi vacancy has effective -3 charge, they neutralize each other.
Thus, it is reasonable to believe that the observed broadening of dielectric peak in Eu
substituted SBT, is due to the oxygen vacancy-induced-dielectric relaxation [60-61, 72] and
not a result of diffused phase transition as in a relaxor ferroelectric since we did not observe
frequency dependence of T
c
for SEBT.
The fall in Curie temperature for SEBT samples can be understood in terms of the observed
tetragonal strain variation (inset of Fig. 5c). Tetragonal strain is the internal strain in the
lattice, which is reported to affect the phase transition temperature [52, 73-75]. Smaller value
of strain indicates that lesser amount of thermal energy is required for the phase transition
and therefore a decrease in T
c
is expected with a decrease in the strain, as indeed observed.
Dielectric measurements reported in other works have also shown that the introduction of
Enhanced Dielectric and Ferroelectric Properties of Donor (W
6+
, Eu
3+
)
Substituted SBT Ferroelectric Ceramics

239
rare-earth ions at the A site in various perovskites and layered oxides, decreases ferroelectric
phase transition temperature [76-78]. Curie temperature of Pr substituted SBT has been
reported to be lower than that of SBT [77]. Dielectric measurements of La-substituted PbTiO
3

have revealed a decrease in T
c
[79]. It is also reported that with increasing La content in SBT,
the dielectric peak broadens and the Curie temperature decreases [42]. Nd has been
substituted at A-site in Bi
4
Ti
3
O
12
(BIT) which resulted in decrease of T
c
[80]. Vaibhav et. al.
[74] have reported that La substitution in SrBi
2
Nb
2
O
9
result in a decrease of T
c
with
broadened peak. Watanabe et. al. [80] reported that lanthanoids like Nd and Pr substitutions
effectively decrease T
c
in BIT. Therefore, since Eu is a rare-earth ion, it is plausible that with
increase in the content of europium, T
c
decreases with broadened peak around the transition
temperature. In addition, it is also known that the incorporation of cations into (Bi
2
O
2
)
2+

layers reduces their electrostatic influence on the perovskite blocks, which might further
contribute to the lowering of phase-transition [48, 81]. As discussed above, some of the Eu
3+

also occupies the available vacant bismuth sites in the bismuth-oxide layer and therefore a
decrease in the phase transition temperature is observed. Possibly all the above discussed
mechanisms contribute partially to the observed dielectric behavior of the studied
compositions.
Fig. 5(d) shows the temperature dependence of tangent loss at 100 kHz for SEBT samples. It
is observed that europium doping reduces the dielectric loss. The loss of Bi
2
O
3
during
sintering process results in the formation of
o
V
••
in SBT

[82]. The additional charge in case of
donor substituted compounds is compensated through the formation of cation vacancies to
maintain the overall charge neutrality of the unit structure. Similar observations have been
made in rare-earth (La
3+
,Nd
3+
, Ce
3+
, Sm
3+
) substituted SBT [39, 42,76-77 ]. Based on the
above reports and the present observations it is reasonable to believe that the substitution of
trivalent Eu ions for divalent Sr ions results in the formation of cation vacancies at the A
sites. For maintaining the charge neutrality of the unit structure, on the substitution of two
Eu
3+
ions, one A-site (Sr site) remains vacant. The corresponding formation of vacancy can
be represented as:

"
1
2
Sr sr
Null Eu V
•
= + (3)
where
"
Sr
V denotes the strontium vacant site;
Sr
Eu
•
denotes Eu occupying the Sr site. Thus, it
can be inferred that in Eu added SBT, the charge difference between Sr
2+
and Eu
3+
is
compensated by the formation of Sr vacancies
"
Sr
V . Since
"
Sr
V are effectively negatively
charged and
o
V
••
are effectively positively charged, these
"
Sr
V reduce the number of
o
V
••
and
thereby reduce the dielectric loss.
3.4 dc conductivity
The electrical conductivity of ceramic materials encompasses a wide range of values. The
conductivity is usually strongly dependent upon temperature and composition [83]. In
insulators charge carriers are regarded as defects in the perfect crystalline order, and the
consideration of charge transport leads necessarily to consideration of point defects and
their migration [84].
Pure SBT has inherent oxygen vacancies that are effectively doubly positively charged, and
thus behave as acceptor-excess material [85]. The apparent net excess of acceptor content in
Ferroelectrics

240
pure SBT can be suppressed by addition of donors that reduces the oxygen vacancy
concentration [85]. It has been reported that conductivity in Bi
4
Ti
3
O
12
(BIT) can be
significantly decreased with the addition of donors, such as Nb, Sb and Ta [86-88]. Makovec
et. al. [39] reported that the minimum conductivity in air-sintered BaBi
4
Ti
4
O
15
ceramics was
obtained by the substitution of ~ 5 mol% of the Ti
4+
ions with Nb
5+
donors, and this resulted
in a conductivity decrease of two orders of magnitude. Therefore, it is reasonable to believe
that the conductivity in SBT can be suppressed by donor addition.
Fig. 6(a) and (b) shows the temperature dependence of dc conductivity (
dc
σ ) for SBTW and
SEBT samples, respectively. The curves show that the conductivity increases with
temperature. This suggests the presence of negative temperature coefficient of resistance
(NTCR), which is a characteristic of insulators [84]. It is observed that d.c. conductivity
reduces with both W and Eu substitution in SBT. Two predominant conduction mechanisms
indicated by slope changes in two different temperature regions are observed. Such change
in the slope in the vicinity of the Curie temperature is attributed to the differences in the
activation energy values in the ferroelectric and paraelectric regions. The temperature
region of ~300 ˚C to ~700 ˚C in these ceramics corresponds to the intrinsic ionic conduction
range [86, 89]. In Table 2 the activation energies in the intrinsic conduction region,
calculated using the Arrhenius equation for all the studied samples are given. The E
a
value
of the W and Eu substituted samples is much higher than that of the pure sample.
1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6
-30
-27
-24
-21
-18
-15
-12
l
n

241
It is known that the major disadvantage of the layer-structured perovskite materials for
certain applications is their relatively high conductivity [90]. The high conductivity
observed in layer-structured perovskite materials is related to the presence of oxygen
vacancies which are effectively positively charged defects or acceptor impurities. The
concentration of these defects and, consequently, the material’s conductivity, thus, increases
by acceptor doping and decreases by donor doping [83-84, 89, 91-93]. Similarly in our case
we observed a decrease in conductivity with donor (W and Eu) substitution in SBT. The
constraint of maintaining the overall charge neutrality of the structure generates cation
vacancies at Sr sites. These cation vacancies thus formed (represented by Eqs. 1 and 3),
effectively reduces the concentration of oxygen vacancies. The effect of both W and Eu
substitution on the concentration of oxygen vacancies is verified from the dc conductivity
measurements since a decrease in dc conductivity is observed in both cases.
It is observed in Table 2 that the E
a
values increases with increasing Eu content. As the
concentration of Eu increases, more and more oxygen vacancies are compensated for and
thereby the energy needed for the charge carriers to migrate (by hopping) also increases,
leading to higher activation energy. As a result, the conductivity decreases because there are
fewer oxygen vacancies available with sufficient energy to move around and the energy
barrier between the scarcer vacancies increases [86]. Whereas in W-substituted samples E
a
is
observed to increase with W concentration up to x = 0.05; however, beyond that it decreases
(Table 2). The decrease in the activation energy for samples with x > 0.05 suggests an
increase in the concentration of mobile charge carriers [94]. This observation can be ascribed
to the existence of multiple valence states of tungsten. Since tungsten is a transition element,
the valence state of W ions in a solid solution most likely varies from W
6+
to W
4+
depending
on the surrounding chemical environment [95-96]. When W
4+
are substituted for Ta
5+
sites,
oxygen vacancies would be created, i.e. one oxygen vacancy would be created for every two
tetravalent W ions entering the crystal structure increasing the concentration of mobile
charge carriers and consequently a decrease in the E
a
beyond x > 0.05.
The observed variation in conductivity with tungsten and europium content in SBT is
consistent with dielectric loss, which also reduces with increasing tungsten concentration
and has been explained in light of contribution from oxygen vacancies.
3.5 Ferroelectric properties
The P-E loops measured at 50 Hz and room temperature for SBTW and SEBT

samples are
shown in Fig. 7 (a) and (b), respectively. It is observed that W-substitution results in the
formation of well-defined hysteresis loops. The optimum tungsten content for maximum 2P
r

(~ 25 μC/cm
2
) is observed to be x = 0.075.
It is known that ferroelectric properties are affected by compositional modification,
microstructure and lattice defects like oxygen vacancies within the structure of the materials
[15-26, 97]. In hard ferroelectrics, with lower-valent substituents the associated oxide
vacancies are likely to assemble in the vicinity of domain walls [43, 98-99]. These domains
are locked by the defects and their polarization switching is difficult, leading to a decrease
in P
r
and an increase in E
c
. Moreover, theoretical calculations [100] have also shown that the
increase in space charge density brings about a decrease in P
r
. On the other hand, in soft
ferroelectrics, with higher-valent substituents, the defects are cation vacancies whose
Ferroelectrics

242
mobility is extremely low below T
c
. Thus, the interaction between cation vacancies and
domain walls is much weaker than that in hard ferroelectrics [38, 43] leading to an increase
in P
r
values. Watanabe et. al. [101] reported a remarkable improvement in ferroelectric
properties in the Bi
4
Ti
3
O
12
ceramic by adding higher valent cation, V
5+
at the Ti
4+
site.
Recently, significantly large P
r
value has been reported for W-substituted BIT sintered
sample [102]. It has also been reported that cation vacancies generated by donor doping
make domain motion easier and enhance the ferroelectric properties [103]. Also it is known
that domain walls are relatively free in large grains and are inhibited in their movement as
the grain size decreases [45]. In the larger grains, domain motion is easier which results in
larger P
r
[104-105].
Based on the obtained results and above discussion, it can be understood that in pure SBT,
the oxygen vacancies assemble at sites like domain boundaries leading to a strong domain
pinning. Hence well-saturated P-E loops for pure SBT are not obtained. Whereas, in the W-
substituted samples, the associated cation vacancy formation suppresses the concentration
of oxygen vacancies. A reduction in the number of oxygen vacancies reduces the pinning
effect on the domain walls, leading to enhanced remnant polarization and lower coercive
field. Another possible reason could be attributed to the increase in grain size of SBTW, as
observed in SEM micrographs (Fig. 3). In the present study, the grain size is observed to
increase with increasing W concentration; however, the remanent polarization does not
monotonously increase with increasing W concentration (Fig. 7a). It is observed that
beyond x > 0.075 P
r
values decreases. Therefore, besides the effect of grain size and
reduction in oxygen vacancies, other factors also influence variation in remnant
polarization.
The decrease in the value of 2P
r
for x > 0.075, seems possibly due to the presence of
secondary phases (observed in XRD diffractograms) which hampers the switching process
of polarization [106-110]. Also this could be explained on the basis of the inference drawn
w.r.t. dc conductivity study in SBTW. We concluded that beyond x > 0.05, the number of
charge carriers increases in the form of oxygen vacancies. This increase in oxygen vacancies
beyond x > 0.05 leads to pinning of domain walls and thus a reduction in the P
r
values is
observed [111].
Fig. 7 (b) shows the P-E loops of the SEBT samples. It is observed that the remanent
polarization increase with increase in europium content. The maximum 2P
r
~14 μC/cm
2
is
observed in the sample with x = 0.20. A lot of studies on the influence of rare-earth ion
substitution in simple perovskite ferroelectrics have shown improved ferroelectric
properties [88, 112-115]. The substitution of smaller lanthanoid ions like Samarium (Sm
3+
),
Neodium (Nd
3+
) and lanthanum (La
3+
) etc. into BIT is reported to enhance remnant
polarization [25, 116-118]. SrBi
4
Ti
4
O
15
, which has a crystalline structure similar to BIT, is
another typical BLSF (m = 4) that shows enhanced ferroelectric properties as a result of La
doping [119]. Noguchi et. al. [76] have reported that La, Nd, and Sm substitution in SBT
show a large P
r
compared to pure SBT. These results suggest that the smaller rare earth ion
substitution enhances ferroelectric properties. Also, the substitution of Sr
2+
by Eu
3+
in the
SBT lattice, results in the formation of vacancies at the A site (
''
Sr
V ) that suppresses the
concentration of oxygen vacancies leading to the observed enhancement of remnant
polarization (Fig. 7b).
Enhanced Dielectric and Ferroelectric Properties of Donor (W
6+
, Eu
3+
)
Substituted SBT Ferroelectric Ceramics

Fig. 7. P-E hysteresis loops for (a) SBTW and (b) SEBT samples
3.6 Piezoelectric studies
Piezoelectric ceramics are widely used for electromechanical transducers and hydrostatic
sensing applications. Among the available materials, lead zirconate titanate (PZT) exhibits a
large piezoelectric coefficient, d
33
(400–600 pC/N) [120]. In recent years, lead-free materials
such as bismuth-layered structured ferroelectrics (BLSFs) have been attracting attention for
piezoelectric device applications, and are found suitable for fine tolerance resonators with
excellent frequency stability [121]. Ando et. al. [122] have reported the effects of
Ferroelectrics

244
compositional modifications in strontium bismuth niobate (SBN)-based BLSF materials in
improving the piezoelectric properties. Kholkin et. al. [43] has reported on the
electromechanical properties of SBT but the maximum polarization and piezoelectric
coefficient that were measured were quite small. Since BLSFs generally have high Curie
temperature and high coercive field at room temperature, it is necessary to perform poling
at high temperature [123]. However, relatively high conductivity often prevents the
application of high electrical field during the high-temperature poling treatment [123-124].
The conductivity, therefore, should be reduced in BLSFs to increase the poling efficiency.
0.00 0.05 0.10 0.15 0.20
12
14
16
18
20
22
24
d
3
3

245
Fig. 8(a) and (b) shows the variation of piezoelectric charge coefficient d
33
with x in SBTW
and SEBT samples, respectively. The d
33
increases with x up to x = 0.05, however, d
33
did not
improve significantly. A decrease in d
33
values is observed for the samples with x > 0.05.
The piezoelectric coefficient, d
33
, increases from 13 pC/N in the sample with x = 0.0 to 23
pC/N in the sample with x = 0.05 in SBTW. Whereas in SEBT samples, the coefficient is
observed to increase from 13 (x =0.0) to 20 pC/N (x = 0.20). The above observation can be
explained on the basis of conductivity behavior observed in W- and Eu-substituted SBT
samples. As observed, electrical conductivity reduces with both donor substituents ( Fig. 6a
and b) in SBT. This decrease in conductivity upon donor substitution improves the poling
efficiency and thus higher d
33
values are obtained. It has also been reported that the
incorporation of higher valent ions accompanied with cation vacancies at the A site in
BLSFs, improves not only the ferroelectric property but also the piezoelectric one [49, 125].
The piezoelectric constants have also been found to increase with increase in grain size [49].
The report that the vacancies at A sites improve the piezoelectric properties due to increased
wall mobility, supports the present observation in both cases. Moreover, since the grain size
increases with both W and Eu content (Figs. 3 and 4), it is reasonable to believe that the
increase in grain size will also contribute to the increase in d
33
values. The decrease in the
value of d
33
for samples with x > 0.05 in SBTW samples is possibly due to the presence of
secondary phases [1, 126-127] in the samples discussed earlier with respect to XRD
observations (Fig. 2a).
4. Conclusions
The addition of tungsten in SBT is observed to be effective in improving dielectric, electrical,
ferroelectric and piezoelectric properties. The X-ray diffractograms show the formation of
the single phase layered structure up to W concentration x ≤ 0.05, beyond which an
unidentified peak is observed though its intensity is very small. Scanning Electron
Microscopy (SEM) photographs reveal that W addition in SBT is effective in improving the
microstructure, as, well developed dense microstructure with large grains are seen. The
average grain size increases with increase in W content. The substitution of the smaller W
6+

ions for Ta
5+
ions in SBT is found to be effective in improving the dielectric properties.
Dielectric constant (
r
ε ) and the Curie temperature (T
c
) increases with increasing W content.
The dielectric loss reduces significantly with increase in doping level. The maximum T
c
of ~
390 ˚C is observed in the sample with x = 0.20 as compared to ~ 320 ˚C for the pure sample.
The peak -
r
ε increases from ~ 270 in the sample with x = 0.0 to ~ 700 for the composition
with x = 0.20. The temperature dependence of the electrical conductivity shows that
tungsten doping results in the decrease of conductivity by as much as 2-3 orders of
magnitude compared to pure SBT. All the tungsten-doped ceramics have higher 2P
r
than
that in the pure sample. The maximum 2P
r
(~25 μC/cm
2
) is obtained in the composition
with x=0.05. The d
33
values increase with increasing W content up to x ≤ 0.05. The value of
d
33
in the composition with x = 0.05 is ~ 23 pC/N as compared to ~ 13 pC/N in the pure
sample.
For the europium-substituted samples, the single phase structure is maintained for the
entire concentration range. The lattice parameters decrease with increase in europium
concentration. The average grain size increases with increasing Eu concentration. It is
Ferroelectrics

250
[124] C. Moure, L. Lascano, J. Tartaj and P. Duran, Ceram. Int., 29, 91 (2003).
[125] C. Fujioka, R. Aoyagi, H. Takeda, S. O. Kamura and T. Shiosaki, J. Eur. Ceram. Soc., 25,
2723 (2005).
[126] R. Jain, V. Gupta, A. Mansingh and K. Sreenivas, Mater. Sci. Engg., B112, 54 (2004).
[127] R. Jain, A. K. S. Chauhan, V. Gupta and K. Sreenivas, J. Appl. Phys., 97, 124101 (2005).
Part 2
Ferroelectrics and Its Applications:
A Theoretical Approach
15
Non-Equilibrium Thermodynamics of
Ferroelectric Phase Transitions
Shu-Tao Ai
Linyi Normal University
People’s Republic of China
1. Introduction
It is well known that the Landau theory of continuous phase transitions is a milestone in the
process of the development of phase transition theories. Though it does not tally with the
nature of phase transitions in the critical regions, the Landau theory as a phenomenological
one has been very successful in many kinds of phase transitions such as the ferroelectric
phase transitions, i.e. the vast studies centering on it have been carried out. In the
ferroelectric case, we should pay attention to the Landau theory extended by A.F.
Devonshire to the first-order phase transitions (Devonshire, 1949; Devonshire, 1951;
Devonshire, 1954). This daring act was said to be successful.
However, the Landau theory is based on the equilibrium (reversible) thermodynamics in
essence. Can it deal with the outstanding irreversible phenomenon of first-order ferroelectric
phase transitions, which is the “thermal hysteresis”? The Landau-Devonshire theory attributes
the phenomenon to a series of metastable states existing around the Curie temperature T
C
. In
principle, the metastable states are not the equilibrium ones and can not be processed by using
the equilibrium thermodynamics. Therefore, we believe that the extension of Devonshire is
problematic though it is successful in mathematics. The real processes of phase transition were
distorted. In Section 2, we will show the unpleasant consequence caused by the metastable
states hypothesis, and the evidence for the non-existence of metastable states, i.e. the logical
conflict. Then in Section 3, we will show the evidence (experimental and theoretical) for the
existence of stationary states to a ferroelectric phase transition. In Section 4 and 5, we will give
the non-equilibrium (irreversible) thermodynamic description of phase transitions, which
eliminates the unpleasant consequence caused by the metastable states hypothesis. At last, in
Section 6 we will give the non-equilibrium thermodynamic explanation of the irreversibility of
ferroelectric phase transitions, i.e. the thermal hysteresis and the domain occurrences in
ferroelectrics.
2. Limitations of Landau-Devonshire theory
The most outstanding merit of Landau-Devonshire theory is that the Curie temperature and
the spontaneous polarization at Curie temperature can be determined simply. However, in
the Landau-Devonshire theory, the path of a first-order ferroelectric phase transition is
believed to consist of a series of metastable states existing around the Curie temperature T
C
.
This is too difficult to believe because of the difficulties encountered (just see the following).
Ferroelectrics

254
2.1 Unpleasant consequence caused by metastable states hypothesis
Basing on the Landau-Devonshire theory, we make the following inference. Because of the
thermal hysteresis, a first-order ferroelectric phase transition must occur at another
temperature, which is different from the Curie temperature. The state corresponding to the
mentioned temperature (actual phase transition temperature) is a metastable one. Since the
unified temperature and spontaneous polarization can be said about the metastable state,
we neglect the heterogeneity of system actually. In other words, every part of the system, i.e.
either the surface or the inner part, is of equal value physically. When the phase transition
occurs at the certain temperature, every part of the system absorbs or releases the latent heat
simultaneously by a kind of action at a distance. (The concept arose in the electromagnetism
first. Here, it maybe a kind of heat transfer). Otherwise, the heat transfer in system, with a
finite rate, must destroy the homogeneity of system and lead to a non-equilibrium
thermodynamic approach. The unpleasant consequence, i.e. the action at a distance should
be eliminated and the life-force should be bestowed on the non-equilibrium thermodynamic
approach.
In fact, a first-order phase transition process is always accompanying the fundamental
characteristics, called the co-existence of phases and the moving interface (phase boundary).
This fact reveals that the phase transition at various sites can not occur at the same time. Yet,
the phase transition is induced by the external actions (the absorption or release of latent
heat). It conflicts sharply with the action at a distance.
2.2 Evidence for non-existence of metastable states: logical conflict
In the Landau-Devonshire theory, if we neglect the influence of stress, the elastic Gibbs
energy
1
G can be expressed with a binary function of variables, namely the temperature
T and the electric displacement D (As
1
G is independent of the orientation of D , here we
are interested in the magnitude of D only)

1 1
1
d d d 0
g g
G T D
T D
∂ ∂
− − =
∂ ∂
(3)
In the Landau-Devonshire theory, the scleronomic constraint equation, i.e. Equation (1) is
expressed in the form of the power series of D (For simplicity, only the powers whose orders
are not more than six are considered)

255
phase transition ferroelectrics is represented graphically in Figure 1. The electric
displacements which correspond with the bilateral minima of
1
G are identified as
*
D ± , and
the electric displacement which corresponds with the middle minimum of
1
G equals zero.
The possible electric displacements should be the above ones which correspond with all the
minima of
1
G .

Fig. 1. The relation between elastic Gibbs energy
1
G and zero field electric displacement D
belongs to the ferroelectrics at various temperatures, which undergoes a first-order phase
transition (Zhong, 1996).
Equivalently, imposed on the generalized displacements
1
, , G T D is a constraint, which is

1
min G = (7)
for certain T. Then, the metastable states are excluded. Thus, the thermal hysteresis does not
come into being. The corollary conflicts with the fact sharply. This reveals that the first-order
ferroelectric phase transition processes must not be reversible at all so as not to be dealt with
by using the equilibrium thermodynamics.
Ferroelectrics

256
How can this difficulty be overcome? An expedient measure adopted by Devonshire is that
the metastable states are considered. However, do they really exist?
Because the metastable states are not the equilibrium ones, the relevant thermodynamic
variables or functions should be dependent on the time t . In addition, the metastable states
are close to equilibrium, so the heterogeneity of system can be neglected. Here, the elastic
Gibbs energy
1
G′ should be
( )
1 2
, , G g T D t ′ = (8)
For the same reason as was mentioned above, Equation (8) can be regarded as a rheonomic
constraint on the generalized displacements
1
, , G T D ′
( ) ( )
2 1 1 2
, , , , , 0 f G T D t G g T D t ′ ′ = − = (9)
In this case, the possible displacements
1
d ,d G T ′ and dD satisfy the following equation

2 2 2
1
d d d d 0
g g g
G T D t
T D t
∂ ∂ ∂
′ − − − =
∂ ∂ ∂
(10)
Comparing Equation (3) with Equation (10), we may find that the possible displacements
here are not the same as those in the former case which characterize the metastable states for
they satisfy the different constraint equations, respectively. (In the latter case, the possible
displacements are time-dependent, whereas in the former case they are not.). Yet, the
integral of possible displacement dD is the possible electric displacement in every case. The
possible electric displacements which characterize one certain metastable state vary with the
cases. A self-contradiction arises. So the metastable states can not come into reality.
What are the real states among a phase transition process? In fact, both the evolution with
time and the spatial heterogeneity need to be considered when the system is out of
equilibrium (Gordon, 2001; Gordon et al., 2002; Ai, 2006; Ai, 2007). Just as what will be
shown in Section 3, the real states should be the stationary ones, which do not vary with the
time but may be not metastable.
3. Real path: existence of stationary states
The real path of a first-order ferroelectric phase transition is believed by us to consist of a
series of stationary states. At first, this was conjectured according to the experimental
results, then was demonstrated reliable with the aid of non-equilibrium variational
principles.
3.1 Conjecture of stationary states based on experiments
Because in the experiments the ferroelectric phase transitions are often achieved by the
quasi-static heating or cooling, we conjectured that they are stationary states processes (Ai,
2006). The results on the motion of interface in ferroelectrics and antiferroelectrics support
our opinion (Yufatova et al., 1980; Dec, 1988; Dec & Yurkevich, 1990). From Figure 2, we
may find that the motion of interface is jerky especially when the average velocity v
a
is
small. A sequence of segments of time corresponding to the states of rest may be found. This
reveals that in these segments of time (characteristic time of phase transition) the stationary
Non-Equilibrium Thermodynamics of Ferroelectric Phase Transitions

257

Fig. 2. The position of phase boundary as a function of time for NaNbO
3
single crystal for
the various values of average velocity v
a
(the values in μm/s given against the curves). (Dec
& Yurkevich, 1990).
distributions of temperature, heat flux, stress, etc. may be established. Otherwise, if the
motion of interface is continuous and smooth, with the unceasing moving of interface
(where the temperature is T
C
) to the inner part, the local temperature of outer part must
change to keep the temperature gradient T ∇ of this region unchanged for it is determined
by l T ρ κ ′ ± = = − ∇
diff
q
v J , where l is the latent heat (per unit mass), ρ is the mass density, ′ v
is the velocity of interface (where the phase transition is occurring),
diff
q
J is the diffusion of
heat, i.e. heat conduction, κ is the thermal conductivity (and maybe a tensor). Then, the
states are not stationary.
3.2 Theoretical evidence based on non-equilibrium variational principles
The non-equilibrium variational principles are just the analogue and generalization of the
variational principles in the analytical dynamics. The principle of least dissipation of energy,
the Gauss’s principle of least constraint and the Hamiltonian prinple etc. in the non-
equilibrium thermodynamics play the fundamental roles as those in the analytical
dynamics. They describe the characteristics of stationary states or determine the real path of
non-equilibrium processes.
For the basic characteristic of non-equilibrium processes is the dissipation of energy, we
define the dissipation function φ as

s
φ σ π = − (11)
where
s
σ is the rate of local entropy production and π is the external power supply (per
unit volume and temperature). Let { }
i
λ λ = represents the set of extensive, pseudo-
thermodynamic variables and its derivative with the time t , i.e. λ

represents the
thermodynamic fluxes. And we define a thermodynamic force
Ti
X and a dissipative force
Di
X as
Ferroelectrics

258
( )
s
Ti
i
X
σ
λ
λ
∂
=
∂

(12)

( ) Di
i
X
φ
λ
λ
∂
=
∂

(13)
Let { }
i
ξ ξ = represent the deviation from a given non-equilibrium stationary state and
provided it is small

(26)
(sum up with respect to i). Due to the minimum entropy production at stationary states, the
linear variation in the entropy production should be zero
0
s
δσ = (27)
Similarly, the power function π can be expanded about the stationary state, i.e.

( ) 1
i i Ei
V χ ξ = (38b)
(not sum up with respect to i ). Henceforth, we will make some discussions in two cases
separately.
No external power supply. Then
0
Ei
X = (39)
According to Equation (35), at second order level, we have

261
( )
2
0
i
i
S
t
R
i i
e ξ ξ = (41)
where ( ) 0
i
ξ is the initial value of
i
ξ . Equation (41) defines the real path with the addition
that
i
R should be a suitable value
*
i
R . It can be determined by Equations (34) and (41)

( )
( )
0
*
0
2
Ti
i
i
R
χ
λ
= −

(42)
The external power supply exists. Similarly, we can obtain the evolution of deviation
i
ξ
( )
( ) 2
0
i i
i
S V
t
R
i i
e ξ ξ
−
= (43)
If ,
i i
V R assume the suitable values
** **
,
i i
V R , the system choose a real path. They can be
determined by Equations (34) and (43)

( )
( )
0
**
0
Ei
i i
Ti
V S
χ
χ
= (44)

( ) ( )
( )
( )
0 0
**
0
2
Ei Ti
i
i
R
χ χ
λ
−
=

(45)
(in every equation from Equation (39) to (45), not sum up with respect to i ).

Fig. 3. Three types of regions and their interfaces in the ferroelectric-paraelectric system in
which a first-order phase transition is occurring. (Ai et al., 2008)
Both the real paths in the two cases reveal that the deviations decrease exponentially when
the system regresses to the stationary states. Stationary states are a kind of attractors to non-
equilibrium states. The decreases are steep. So the regressions are quick. It should be noted
that we are interested in calculating the change in the generalized displacements during a
Ferroelectrics

262
macroscopically small time interval. In other words, we are concerned with the
determination of the path of an irreversible process which is described in terms of a finite
difference equation. In the limit as the time interval is allowed to approach zero, we obtain
the variational equation of thermodynamic path.
So, if the irreversible process is not quick enough, it can be regarded as the one that consists
of a series of stationary states. The ferroelectric phase transitions are usually achieved by the
quasi-static heating or cooling in the experiments. So, the processes are not quick enough to
make the states deviate from the corresponding stationary states in all the time. In Figure 3,
three types of regions and their interfaces are marked I, II, III, 1, 2 respectively. The region
III where the phase transition will occur is in equilibrium and has no dissipation. In the
region I where the phase transition has occurred, there is no external power supply, and in
the region II (i.e. the paraelectric-ferroelectric interface as a region with finite thickness
instead of a geometrical plane) where the phase transition is occurring, there exists the
external supply, i.e. the latent heat (per unit volume and temperature). According to the
former analysis in the two cases, we may conclude that they are in stationary states except
for the very narrow intervals of time after the sudden lose of phase stability.
4. Thermo-electric coupling
In the paraelectric-ferroelectric interface dynamics induced by the latent heat transfer
(Gordon, 2001; Gordon et al., 2002), the normal velocity of interface
n
v was obtained
( ) ( )
1
n fer par
fer par
v k T k T
lρ
⎡ ⎤
= ∇ − ∇ ⋅
⎢ ⎥
⎣ ⎦
n (46)
where l is the latent heat (per unit mass), ρ is the density of metastable phase (paraelectric
phase),
fer
k is the thermal conductivity coefficient of ferroelectric phase,
par
k is the thermal
conductivity coefficient of paraelectric phase, ( )
fer
T ∇ is the temperature gradient in
ferroelectric phase part, ( )
par
T ∇ is the temperature gradient in paraelectric phase part, n is
the unit vector in normal direction. The temperature gradients can be studied from the point
of view that a ferroelectric phase transition is a stationary, thermo-electric coupled transport
process (Ai, 2006).
4.1 Local entropy production
In the thermo-electric coupling case, the Gibbs equation was given as the following
d d d d
i i
i
T s u n μ = − ⋅ −
∑
E D (47)
where , , T E D is the temperature, the electric field intensity and the electric displacement
within a random small volume, respectively; , , ,
i i
s u n μ is the entropy density, the internal
energy density, the chemical potential and the molar quantity density in the small volume,
respectively. And there, it was assumed that the crystal system is mechanically-free (No
force is exerted on it). Differentiating Equation (47) and using the following relations
0
u
t
∂
+ ∇⋅ =
∂
J
u
(48)
Non-Equilibrium Thermodynamics of Ferroelectric Phase Transitions

s
s
t
σ
∂
+ ∇⋅ =
∂
J
s
(57)
This is the local entropy balance equation. We know, the system is in the crystalline states
before and after a phase transition so that there is no diffusion of any kind of particles in the
system. So, 0 = J
ni
. The local entropy production can be reduced as

1
s
T T
φ
σ
⎛ ⎞ ⎛ ⎞
= ⋅ ∇ + ⋅ ∇
⎜ ⎟ ⎜ ⎟
⎝ ⎠ ⎝ ⎠
J J
q P
(58)
We know the existence of ferroics is due to the molecular field. It is an inner field. So we
must take it into account. Here, the electric field should be the sum of the outer electric field
E
o
and the inner electric field E
i

Ferroelectrics

264
= + E E E
o i
(59)
Correspondingly, there are the outer electrical potential
o
φ and the inner electrical potential
i
φ and they satisfy

o
φ = −∇ E
o
(60)

i
φ = −∇ E
i
(61)
If the outer electric field is not applied,
o
φ can be a random constant. There is no harm in
letting the constant equal to zero. Then the entropy production equals

265
If there is no restriction on X
q
and X
P
, according to the conditions on which the entropy
production is a minimum
0
s
σ
⎛ ⎞
∂
⎜ ⎟ = ⋅ + ⋅ = =
⎜ ⎟
∂
⎝ ⎠
X
2L X 2L X 2J
X
P
qq q qP P q
q
(69)
0
s
σ
⎛ ⎞
∂
= ⋅ + ⋅ = =
⎜ ⎟
⎜ ⎟
∂
⎝ ⎠
X
2L X 2L X 2J
X
q
Pq q PP P P
P
(70)
we know the stationary states are equilibrium ones actually. If we let X
q
(or X
P
) be a
constant, according to Equation (70) (or (69)) we know J
P
(or J
q
), which is corresponded
with another force X
P
(or X
q
), should be zero.
Then, a first-order ferroelectric phase transition can be described by the second paradigm.
Since the force X
P
of the region where the phase transition is occurring is a large constant,
the flux J
q
of the region should be zero (but 0 ≠ J
P
). This states clearly that the pure heat
conduction and the heat conduction induced by the thermo-electric coupling cancel out each
other so as to release or absorb the latent heat. It is certain that the latent heat passes through
the region where the phase transition has occurred (at the outside of the region where the
phase transition is occurring) and exchanges itself with the thermal bath. Accompanied with
the change of the surface’s temperature and the unceasing jerky moving of the region where
the phase transition is occurring, a constant temperature gradient is kept in the region where
the phase transition has occurred, i.e. the force X
q
is a constant. So, the flux 0 = J
P
(but
0 ≠ J
q
). This states clearly that the electric displacement of the region where the phase
transition has occurred will not change but keep the value at Curie temperature or zero until
the phase transition finishes. Differently, the region where the phase transition will occur
should be described by the first paradigm for there is no restriction on the two forces
X , X
P q
. The states of this region are equilibrium ones. So the temperature gradient T ∇
should be zero.
4.3 Verification of interface dynamics
Considering that ( ) 0
par
T ∇ ≈ for the region where the phase transition will occur (i.e. the
paraelectric phase part) can be regarded as an equilibrium system, we modify equation (46) as

( )
fer
fer
n
k T
v
lρ
∇ ⋅
=
n
(71)
In order to compare it with experiments, we make use of the following values which are
about PbTiO
3
crystal: ρ =7.1g/cm
3
(Chewasatn & Milne, 1994), l =900cal/mol (Nomura &
Sawada, 1955),
fer
k =8.8× 10
5
erg/cm﹒s﹒K (Mante & Volger, 1967). The value of the
velocity of the interface’s fast motion, which has been measured by the experiments, is
0.5mm/s (Dec, 1988). According to equation (71), we calculate the corresponding
temperature gradient to be 57.35K/cm. However, in (Dec, 1989) it is reported that the
experimental temperature gradient varies from 1.5 to 3.5K/mm while the experimental
velocity of interface’s motion varies from 732 to 843μm/s. Considering the model is rather
rough, we may conclude that the theory coincides with the experiments.
Ferroelectrics

266
5. Thermo-electro-mechanical coupling
The comprehensive thermo-electro-mechanical coupling may be found in the ferroelectric
phase transition processes. Because there exists not only the change of polarization but also
the changes of system’s volume and shape when a ferroelectric phase transition occurs in it,
the mechanics can not be ignored even if it is mechanically-free, i.e. no outer force is exerted
on it. To a first-order ferroelectric phase transition, it occurs at the surface layer of system
firstly, then in the inner part. So, the stress may be found in the system.
Since one aspect of the nature of ferroelectric phase transitions is the thermo-electro-
mechanical coupling, we take the mechanics into account on the basis of Section 4, where
only the thermo-electric coupling has been considered. This may lead to a complete
description in the sense of continuum physics. In this section, the mathematical deducing is
reduced for it is complicated. The details may be referred in (Ai, 2007).
5.1 Deformation mechanics
For a continuum, the momentum equation in differential form can be written as
ρ ρ ∇⋅ + = σ f a (72)
where , ρ σ, f,a is the stress, the volume force exerted on unit mass, the acceleration and the
mass density, respectively. Let
2 1
2
k = v be the local kinetic energy density (per unit mass),
with v is the velocity. Then

real nom
= + σ σ σ (79)
The nominal volume force and stress are not zero until the eigen (free) deformation of
system finishes in phase transitions. If they are zero, the eigen (free) deformation finishes.
5.2 Local entropy production and description of phase transitions
The Gibbs equation was given as the following
( )
1 1
d d d d d d d
i i
i
T s n t u k μ
ρ ρ
+ + ⋅ + ⋅ + ∇⋅ ⋅ = +
∑
E D f r v σ (80)
where , T E, D is the local temperature, the local electric field intensity and the local electric
displacement, respectively; , , ,
i i
s u n μ is the local entropy density (per unit mass), the local
internal energy density (per unit mass), the local molar quantity density (per unit mass) and
the chemical potential, respectively; r is the displacement vector. If the outer electric field is
not applied, the quantity E is the inner electric field
in
E only (Ai, 2006).
Make the material derivative of Equation (80) with t , then obtain
( )
d d 1 d d 1 d
d d d d d
in i
i
i
n s e
t T t T t T t T T t
ρ ρ ρ
ρ μ + + ⋅ + ⋅ + ∇⋅ ⋅ =
∑
D r
E f v σ (81)
where e is the total energy with e u k = + . We know, the system is in the crystalline states
before and after a phase transition so that there is no diffusion of any kind of particles in the
system. So,
i
n as the local molar quantity (per unit mass) does not change with t , i.e.
0
i
dn
dt
= .
d
dt
D
stands for the polarization current
P
J , while
d
dt
r
stands for the velocity v ,
in in
φ = −∇ E (
in
φ stands for the inner electric potential).
After the lengthy and troublesome deduction (Ai, 2007), we obtain the local entropy balance
equation in Lagrangian form

ij ji
L L = (93)
So the rate of local entropy production can be re-written as

4
, 1
s ij i j
i j
L X X σ
=
=
∑
(94)
For convenience, we have modified the superscripts , , , q P f σ to be 1,2,3,4.
In view of Section 3, the states of a ferroelectric phase transition are stationary. So the
principle of minimum entropy production is satisfied. If we keep the former k forces being
constants, i.e.
( ) 1, 2, , , 4
i
X const i k k = = ⋅ ⋅ ⋅ < , the conditions on which the local entropy
production is a minimum are

269
This reveals that the fluxes corresponding to the left 4 k − forces are zero. Of course, if there
are no restrictions on ( ) 1, 2, 3, 4
i
X i = , all the flues are zero.
We may describe a ferroelectric phase transition by using the two paradigms above
similarly as do in Section 4. To a first-order ferroelectric phase transition, the forces
, ,
P f σ
X X X of the region where the phase transition is occurring can be regarded as three
large constants roughly in the characteristic times of phase transition because the electric
displacement, the volume and the shape change suddenly. So, the flux
diff
q
J of the region
should be zero (but 0, 0, 0
P
ρ ≠ ≠ ≠ J σ f ). This states clearly that the pure heat conduction
and the heat conduction induced by the thermo-electric coupling and the thermo-
mechanical coupling cancel out each other so as to release or absorb the latent heat. The
phase transition occurs at the surface layer firstly, which is mechanically-free. So, when the
phase transition occurs in this region, the flux σ maybe the nominal stress
nom
σ only,
which does work to realize the transformation from the internal energy to the kinetic
energy. When the phase transition occurs in the inner part, the flux σ should be the sum of
real
σ and
nom
σ because the sudden changes of inner part’s volume and shape have to
overcome the bound of outer part then
real
σ arises. The region where the phase transition is
occurring, i.e. the phase boundary is accompanied with the real stress
real
σ usually, which
does work to realize the transformation from the kinetic energy to the internal energy. This
has been predicted and described with a propagating stress wave. (Gordon, 1991).
It is certain that the latent heat passes through the region where the phase transition has
occurred (at the outside of the region where the phase transition is occurring) and exchange
itself with the thermal bath. For
diff
a q
l T ρ κ ± = = − ∇ v J , a constant temperature gradient T ∇
is kept in the region where the phase transition has occurrd, i.e. the force
q
X at every site is
a constant (which does not change with the time but may vary with the position). So, the
fluxes 0
P
ρ = = = J σ f (but the flux 0
diff
q
≠ J ). This states clearly that the electric
displacement D will not change but keep the value at Curie temperature or zero until the
phase transition finishes and
real nom
= − σ σ in this region. Because the electric displacement
D and the strain (or deformation) are all determined by the crystal structure of system,
0
P
= J reveals that D of this region does not change so does not the crystal structure then
does not the strain (or deformation). According to (Gordon, 1991), we know the region
where the phase transition has occurred is unstressed, i.e. 0
real
= σ , then 0
nom
= σ . This
reveals that the eigen (free) strain (or deformation) of system induced by the thermo-electro-
mechanical coupling of phase transition is complete and the change of it terminates before
the phase transition finishes. The two deductions coincide with each other.
real
σ may relaxes
via the free surface.
The region where the phase transition will occur should be in equilibrium because there are
no restrictions on the forces , , ,
q P f σ
X X X X . Whereas, according to (Gordon, 1991), the
region is stressed, i.e. 0
real
≠ σ . To the heating process of phase transition, this may lead to a
change of the spontaneous polarization of this region because of the electro-mechanical
coupling (piezoelectric effect).
An immediate result of the above irreversible thermodynamic description is that the action
at a distance, which is the kind of heat transfer at phase transitions, is removed absolutely.
The latent heat is transferred within a finite time so the occurrence of phase transition in the
inner part is delayed. (Of course, another cause is the stress, just see Section 6) In other
Ferroelectrics

270
words, the various parts absorb or release the latent heat at the various times. The action at a
distance does not affect the phase transition necessarily.
5.3 Relation between latent heat and spontaneous polarization
By now, among the latent heat, the spontaneous polarization, the stress and the strain, only
the latent heat and the spontaneous polarization have been measured often for first-order
ferroelectric phase transitions. So, we will consider a simplified case of thermo-electric
coupling only so as to establish the relation between the latent heat and the spontaneous
polarization in the realm of non-equilibrium thermodynamics.
All the quantities of the region where the phase transition has occurred are marked with the
superscript “I”; all the quantities of the region where the phase transition is occurring are
marked with the superscript “II”; and all the quantities of the region where the phase
transition will occur are marked with the superscript “III”. Let’s consider the heating
processes of phase transition firstly. In the region where the phase transition has occurred,

I para I para I para
q qq q a
lρ
− − −
= ⋅ = J L X v (96)
where we have ignored the difference between the mass density of ferroelectric phase and
that of paraelectric phase (almost the same) and denote them as ρ ,
a
v is the average
velocity of interface. In the region where the phase transition is occurring,
0
II II II II II
q qq q qP P
= ⋅ + ⋅ = J L X L X (97)

II II II II II
P Pq q PP P
= ⋅ + ⋅ J L X L X (98)
The heat which is transferred to the region where the phase transition is occurring is
absorbed as latent heat because the pure heat conduction and the heat conduction induced
by the thermo-electric coupling cancel out each other. So,

II II
a qq q
lρ = ⋅ v L X (99)
According to Eq. (97)-(99), we work out

( ) ( )
1 1
II II II II II II
P Pq qq PP qP a P
lρ
− −
⎡ ⎤
′
= − ⋅ − ⋅ ⋅ = −
⎢ ⎥
⎣ ⎦
J L L L L v J (106)
Then we find that
spon III −
P (serves as the equilibrium polarization) is not equal to
spon I −
P
(serves as the non-equilibrium polarization). For the region where the phase transition will
occur is stressed, there is some difference between
( )
spon spon III −
= P P and the equilibrium
spontaneous polarization without the affects of stress
spon′
P because of the piezoelectric
effect.
6. Irreversibility: thermal hysteresis and occurrences of domain structure
6.1 Thermal hysteresis
The “thermal hysteresis” of first-order ferroelectric phase transitions is an irreversible
phenomenon obviously. But it was treated by using the equilibrium thermodynamics for
ferroelectric phase transitions, the well-known Landau-Devonshire theory (Lines &
Glass,1977). So, there is an inherent contradiction in this case. The system in which a first-
order ferroelectric phase transition occurs is heterogeneous. The occurrences of phase
transition in different parts are not at the same time. The phase transition occurs at the
surface layer then in the inner part of system. According to the description above, we know
a constant temperature gradient is kept in the region where the phase transition has
occurred. The temperature of surface layer, which is usually regarded as the temperature of
the whole system in experiments, must be higher (or lower) than the Curie temperature.
This may lead to the thermal hysteresis.
No doubt that the shape and the area of surface can greatly affect the above processes. We
may conclude that the thermal hysteresis can be reduced if the system has a larger specific
surface and, the thermal hysteresis can be neglected if a finite system has an extremely-large
specific surface. So, the thermal hysteresis is not an intrinsic property of the system.
The region where the phase transition will occur can be regarded as an equilibrium system
for there are no restrictions on the forces , , ,
q P f σ
X X X X . In other words, the forces and the
corresponding fluxes are zero in this region. To a system where a second-order ferroelectric
phase transition occurs, the case is somewhat like that of the region where a first-order
ferroelectric phase transition will occur. The spontaneous polarization , the volume and the
shape of system are continuous at the Curie temperature and change with the infinitesimal
magnitudes. This means , , ,
q P f σ
X X X X and , , ,
diff
q P
ρ J J σ f can be arbitrary infinitesimal
magnitudes. The second-order phase transition occurs in every part of the system
Ferroelectrics

272
simultaneously, i.e. there is no the co-existence of two phases (ferroelectric and paraelectric).
So, there is no the latent heat and stress. The thermal hysteresis disappears.
The region where a first-order ferroelectric phase transition will occur is stressed. This
reveals that the occurrences of phase transition in the inner part have to overcome the
bound of outer part, where the phase transition occurs earlier. This may lead to the delay of
phase transition in the inner part.
6.2 Occurrences of domain structure
Though the rationalization of the existence of domain structures can be explained by the
equilibrium thermodynamics, the evolving characteristics of domain occurrences in
ferroelectrics can not be explained by it, but can be explained by the non-equilibrium
thermodynamics.
In the region where the phase transition is occurring, the thermodynamic forces
P
X (=
in
T
φ
⎛ ⎞
∇⎜ ⎟
⎜ ⎟
⎝ ⎠
),
σ
X (=
1
T
⎛ ⎞
− ∇
⎜ ⎟
⎝ ⎠
v ),
f
X (= −
v
T
) can be regarded as three large constants in the
characteristic time of transition and the thermodynamic flux 0 =
diff
q
J (but 0 ≠
P
J , 0 σ ≠ ,
ρ ≠ f 0 ). The local entropy production (cf. Equation (84)) reduces to

and or of
T
−
v
vary continuously such that they are differently oriented at defferent locations.
There are always several (at least two) symmetry equivalent orientations in the prototype
phase (in most cases it is the high temperature phase), which are the possible orientations
for spontaneous polarization (or spontaneous deformation or spontaneous displacement).
Therefore, the spontaneous polarization, the spontaneous deformation and the spontaneous
displacement must take an appropriate orientation respectively to ensure σ
s
is a positive
minimum when the system transforms from the prototype (paraelectric) phase to the
ferroelectric (low temperature) phase. The underlying reasons are that

273
where , , ε L and
0
ε is the modulus of rigidity, the strain and the permittivity of vacuum,
respectively. Therefore, ,ε P at different locations will be differently oriented. The domain
structures in ferroelectrics thus occur.
It seems that the picture of domain occurrences for first-order ferroelectric phase transition
systems should disappear when we face second-order ferroelectric phase transition systems.
This is true if the transition processes proceed infinitely slowly as expounded by the
equilibrium thermodynamics. But any actual process proceeds with finite rate, so it is
irreversible. Then the above picture revives.
In (Ai et al., 2010), the domain occurrences in ferromagnetics can be described parallelly by
analogy. And the case of ferroelastic domain occurrences is a reduced, simpler one
compared with that of ferroelectrics or ferromagnetics.
It is well known that the Landau theory or the Curie principle tells us how to determine the
symmetry change at a phase transition. A concise statement is as follows (Janovec, 1976): for a
crystal undergoing a phase transition with a space-group symmetry reduction from G
0
to G,
whereas G determines the symmetry of transition parameter (or vice versa), it is the symmetry
operations lost in going from G
0
to G that determine the domain structure in the low-
symmetry phase. The ferroic phase transitions are the ones accompanied by a change of point
group symmetry (Wadhawan, 1982). Therefore, the substitution of “point group” for the
“space group” in the above statement will be adequate for ferrioc phase transitions. From the
above statement, the domain structure is a manifestation of the symmetry operations lost at
the phase transition. In our treatment of the domain occurrences in ferroics, we took into
account the finiteness of system (i.e. existence of surface) and the irreversibility of process
(asymmetry of time). The finiteness of system makes the thermodynamic forces such as
1
, ,
in
T
φ
⎛ ⎞
⎛ ⎞
∇ − ∇ − ⎜ ⎟
⎜ ⎟
⎜ ⎟
⎝ ⎠
⎝ ⎠
v
v
T T
have infinite space symmetry. The infinite space symmetry,
combined with the asymmetry of time, reproduces the symmetry operations lost at the phase
transition in the ferroic phase. It can be viewed as an embodiment of time-space symmetry.
After all, for the domain structures can exist in equilibrium systems, they are the
equilibrium structures but not the dissipative ones, for the latter can only exist in systems far
from equilibrium (Glansdorff & Prigogine, 1971).
7. Acknowledgments
I acknowledge the supports of the Natural Science Foundation Programs of Shandong
Province (Grant No. Y2008A36).
8. References
Ai, S.T. (2006). Paraelectric-Ferroelectric Interface Dynamics Induced by Latent Heat
Transfer and Irreversible Thermodynamics of Ferroelectric Phase Transitions.
Ferroelectrics, Vol. 345, No.1, (June, 2006) 59-66, ISSN 1563-5112 (online), 0015-0193
(print).
Ai, S.T. (2007). Mechanical-Thermal-Electric Coupling and Irreversibility of Ferroelectric
Phase Transitions. Ferroelectrics, Vol.350, No.1 (May, 2007) 81-92, ISSN 1563-5112
(online), 0015-0193 (print).
Ai, S.T.; Xu, C.T.; Wang, Y.L.; Zhang, S.Y.; Ning, X.F. & Noll, E. (2008). Comparison of and
Comments on Two Thermodynamic Approaches (Reversible and Irreversible) to
Ferroelectrics

Fig. 1. Free energy for a first order ferroelectric phase transition at different temperatures
There are four characteristic temperatures in the phase transition process, i.e., Curie-Weiss
temperature T
0
, Curie temperature T
c
, ferroelectric limit temperature T
1
and limit temperature
Theories and Methods of First Order Ferroelectric Phase Transitions

277
of field induced phase transition T
2
. The Curie-Weiss temperature can be easily accessed
experimentally from the Curie-Weiss law of dielectric constant ε at paraelectric phase, i.e.,

0
p
C
T T
ε =
−
(3)
In above expression, C is the Curie-Weiss constant, subscript p of ε stands for paraelectric
phase. However the Curie temperature is less accessible experimentally. This temperature
measures the balance of the ferroelectric phase and the paraelectric phase. At this
temperature, the free energy of ferroelectric phase is the same as that of paraelectric phase.
When temperature is between T
0
and T
c
, ferroelectric phase is stable and paraelectric phase
is meta-stable, this can be easily seen in Fig.1. When the temperature is between T
c
and T
1
,
ferroelectric phase is in meta-stable state while paraelectric phase is stable. When the
temperature is higher than T
1
, ferroelectric phase disappears. Normally, this temperature is
corresponding to the peak temperature of dielectric constant when measured in heating
cycle. In other words, peak temperature of dielectric constant measured in heating cycle is
the ferroelectric limit temperature T
1
, not the Curie temperature T
c
in a more precise sense.
Between temperature T
1
and T
2
, ferroelectric state still can be induced by applying an
external electric field. The polarization versus the electric field strength is a double
hysteresis loop, which is very similar with that observed in anti-ferroelectric materials.
When the temperature is higher than T
2
, only paraelectric phase can exist.
The characteristic temperatures T
c
, T
1
and T
2
can be easily determined from Eq.(2) of free
energy as following. The Curie temperature T
c
can be obtained from the following two
equations;
( )
2 4 6
0 0 11 111
1 1 1
0
2 4 6
c x x x
G T T P P P Δ = α − + α + α = (4)
( )
3 5
0 0 11 111
0
c x x x
x
G
T T P P P
P
∂Δ
= α − + α + α =
∂
(5)
The first equation means that the free energy of ferroelectric phase is same as that of
paraelectric phase, and the second equation implies that the free energy of ferroelectric
phase is in minimum. From above two equations, we can have the expression of the Curie
temperature T
c
as

2
11
0
0 111
3
16
c
T T
α
= +
α α
(6)
At the ferroelectric limit temperature T
1
, free energy has an inflexion point at Ps, the
spontaneous polarization. As can be seen from Fig. 1, when temperature is below T
1
, free
energy has are three minima, i.e., at P=±Ps, and P=0. Above temperature T
1
, there is only
one minimum at P=0. The spontaneous polarization can be obtained from the minimum of
the free energy as,

Fig. 2. Temperature dependence of the spontaneous polarization
Plotting E
x
as a function of P
x
and reflecting the graph about the 45 degree line gives an 'S'
shaped curve when temperature is much lower than the transition temperatures, as can be
seen from curves in Fig. 3. The central part of the 'S' corresponds to a free energy local
maximum, since the second derivative of the free energy ΔG respect polarization P
x
is
negative. Elimination of this region and connection of the top and bottom portions of the 'S'
curve by vertical lines at the discontinuities gives the hysteresis loop. Temperatures are
labeled by each curve, label of 0.7T
0
in Fig. 3 is for temperature T=0.7T
0
, and 1.2T
2
is for
T=1.2T
2
, T
12
stands for T=(T
1
+T
2
)/2. When the temperature is below Curie temperature T
c
,
normal ferroelectric hysteresis loops can be obtained. When the temperature is between T
1

and T
2
, double hysteresis loop or pinched loop could be observed. That means ferroelectric
state is induced by the applied electric field. When the temperature is higher than T
2
, the
polarization versus electric field becomes a non-linear relation, see 1.2T
2
curve in Fig. 3. It
should point out that curves in Fig. 3 are obtained under static electric field. Experimental
Ferroelectrics

280
measurements usually are performed using time dependent electric field, mostly in sine
form. Therefore the hysteresis loops obtained experimentally might be different from the
shapes shown in Fig. 3.

Fig. 3. Static hysteresis loops at different temperatures
Dynamic behavior of ferroelectrics from theoretical simulation could be more helpful for
understanding the experimental observing. The dynamic property of ferroelectrics can be
studied using Landau-Khalantikov equation (Blinc & Zeks, 1974)

dP G
dt P
δΔ
= −Γ
δ
(20)
where Γ is the coefficient of thermodynamic restoring force. This equation has been
employed to investigate the switching characters of asymmetric ferroelectric films (Wang et
al., 1999) and the effects of external stresses on the ferroelectric properties of Pb(Zr,Ti)TiO
3

281
still observed because of the finite value of relaxation time. Higher than T
2
, no hysteresis can
be observed, but a non-linear P-E relation curve. Similar shapes of hysteresis loops have
been observed in Pb
x
Sr
1-x
TiO
3
ceramics recently(Chen et al., 2009).

Fig. 4. Dynamic hysteresis loops at different temperatures with frequency ω=0.001. Dark
loop is at Curie temperature T
c
, red curve is for T
1
, blue curve for (T
1
+T
2
)/2, green curve for
T
2
, and dark line for T=1.2T
2
.
To get insight understanding of the influence of the frequency on the shape of the hysteresis,
more hysteresis loops are presented in Fig. 5. The frequency is set as ω=0.001 for green
curves, ω=0.01 for red curves and ω=0.03 for blue curves at Curie temperature T
c
, T
1
,
(T
1
+T
2
)/2 and at T
2
respectively. At Curie temperature T
c
, see Fig. 5(a), the coercive field
increases with increasing of measure frequency, but the spontaneous polarization is less
influenced by the frequency. At temperature T
1
, this temperature corresponding to the peak
temperature of dielectric constant when measured in heating cycle, pinched hysteresis loop
can be observed at low frequency, see the green curve in Fig. 5(b). At higher frequency, the
loop behaves like a normal ferroelectric loop, see blue curve in Fig.5(b). When temperature
is between T
1
and T
2
, as shown in Fig. 5(c) for temperature at T=(T
1
+T
2
)/2, typical double
hysteresis loop can be observed at low frequency. When the frequency is higher, it becomes
a pinched loop. This trend of loop shape can be kept even when temperature is up to T
2
, see
curves in Fig. 5(d).
Temperature dependence of polarization at different temperature cycles can be also
obtained from Eq.(21) with a constant electric field E=0.01. The results are shown in shown
in Fig. 6 with different Γ, the coefficient of thermodynamic restore force. The dark line is for
the static polarization, red curves are field heating, blue curves are field cooling. Solid lines
are for Γ=100, and dash-dotted lines are for Γ=10. The temperature hysteresis from the static
theory, as indicated by the two dark dash lines, is smaller than that from Landau-
Khalanitkov theory. In other words, temperature hysteresis ΔT measured experimentally
would be usual larger than that from static Landau theory. Also the temperature hysteresis
ΔT depends on Γ, since Γ is related with the relaxation time. A larger Γ represents small
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282
relaxation time, or quick response of polarization with electric field. Hence ferroelectrics
with long relaxation time, i.e., small Γ, would expect a very larger temperature hysteresis.

Fig. 6. Temperature dependence of polarization at different temperature cycles. Dark line is for
the static polarization. Red curves are field heating, blue curves are field cooling. Solid lines
are for short relaxation time(larger Γ), and dash-dot lines are for lone relaxation time (small Γ).
Theories and Methods of First Order Ferroelectric Phase Transitions

283
3. Effective field approach
The effective field approach has proved to be a simple statistic physics method but valuable
way to describe phase transitions (Gonzalo, 2006). The main supposition of this model is
that each individual dipole is influenced, not only by the applied electric field, but by every
dipole of the system. In its simplest form, which takes into account only dipole interactions,
describes fairly well the main features of continuous ferroelectric phase transitions, i.e.
second order phase transition. The inclusion of quadrupolar and higher order terms into the
effective field expression is necessary for describing the properties of discontinuous or first
order phase transitions (Gonzalo et al., 1993; Noheda et al., 1993, 1994). The effective field
approach has turned out to be successful explaining the composition dependence of the
Curie temperature in mixed ferroelectrics systems (Ali et al., 2004; Arago et al., 2006). A
quantum effective field approach has also been developed for phase transitions at very low
temperature (Gonzalo, 1989; Yuan et al., 2003; Arago et al., 2004) in ferro-quantum
paraelectric mixed systems. In this section, quantum effective field approach is adopted to
reveal the influence of the zero point energy on first order phase transitions (Wang et al.,
2008). We can see that when the zero point energy of the system is large enough and the
ferroelectric phase is suppressed, a phase transition-like temperature dependence of the
polarization can be observed by applying an electric field.
The effective field, as described in detail in Gonzalo’s book (Gonzalo, 2006), can be
expressed as

3 5
eff
E E P P P = +β + γ + δ +" (23)
where E is the external electric field, and the following terms correspond to the dipolar,
quadrupolar, octupolar, etc., interaction. By keeping the first two terms, i.e. dipolar and
quadrupolar interaction, gives account of the first order transition.
From statistical considerations, the equation of state is,

3
1
tanh
S S
S
p gp
t
p
−
+
= (28)
Fig.7 shows the plot of the normalized spontaneous polarization p
S
versus normalized
temperature t obtained from Eq. (28) for several values of the parameter g. As it is shown in
the discussion of the role of the quadrupolar interaction in the order of the phase transition
(see Gonzalo et al., 1993; Noheda et al., 1993; Gonzalo, 2006), values of g smaller than 1/3
correspond to a second order, or continuous phase transition, and values larger than 1/3
indicate that the transition is discontinuous, that is, first order. In this case, a spontaneous
polarization p
θ
exists at temperature T
θ
>T
C
, and then τ
θ
>1, being Δt = t
θ
-1 the corresponding
reduced thermal hysteresis, which is the signature of the first order transitions.

( )
3
1
, e 0
tanh / tanh
Q S S
S
p gp
t
t p
−
+ Ω
≡ = =
Ω
(33)
The temperature dependence of the spontaneous polarization can be found from above
equation for a given value of g and different values of the parameter Ω. Fig. 8 plots p
S
(t) with
g = 0.8 to ensure it is a first order transition. The influence of the zero-point energy is quite
obvious: when it is small, the phase transition is still of normal first order one. As the zero
point energy increases, both the transition temperatures and the spontaneous polarization
decrease. The Curie temperature goes to zero for Ω = 1, but no yet t
θ
, neither the saturation
spontaneous polarization does. From the definition of the normalized zero point energy Ω,
we can see then that the Curie temperature goes to zero when the zero point energy is the
same as the classical thermal energy k
B
T
C
. Imposing again the condition of the zero slope,
Ferroelectrics

286
(∂t/∂p
S
)p
θ
= 0, we can obtain p
θ
(Ω), and then t
θ
(Ω), which must be zero when the ferroelectric
behavior will be completely depressed. In this way we work out the zero point energy
critical value (Ω
cf
= 1.1236 for g=0.8) that would not allow any ordered state. Furthermore,
from the condition t
θ
(Ω
cf
, g) = 0, we will find the relationship between the critical zero point
energy Ω
cf
and the strength of the quadrupolar interaction given by the coefficient g. Fig. 9
plots Ω
cf
(g) that indicates that Ω
cf
grows almost linearly with g, specially for larger values of
g. This means that ferroelectrics with strong first order phase transition feature needs a
relative large critical value of zero point energy to depress the ferroelectricity.

Fig. 8. Temperature dependence of the spontaneous polarization at different zero point
energy. All curves correspond to a quadrupolar interaction coefficient g=0.8. (Wang et al.,
2008)
Above results prove that a ferroelectric material, with strong quadrupolar interaction,
undergoes a first order transition (g>1/3) unless its zero point energy reaches a critical
value, Ω
cf
, because in such case the phase transition is inhibited. However, an induced phase
transition must be reached by applying an external electric field. Let be a system with g= 0.8,
and Ω=1.6, that is a first order ferroelectric with a zero point energy above the critical value
and, hence, no phase transition observed. And let us apply a normalized electric field e that
will produce a polarization after Eq. (32). Fig. 10 plots p(t) for different values of the electric
field. It can be seen that when it is weak (see curves corresponding to 0.01 and 0.02), the
polarization attains quickly a saturation value, similar to what is found in quantum
paraelectrics. The curve of e=0.03 (see the dashed line) is split into two parts. The lower part
would represent a quantum paraelectric state, but the upper part stands for a kind of
ferroelectric state. Therefore there exists a critical value between e=0.02 and 0.03, which is
the minimum electric field for inducting a phase transition. For 0.04<e<0.06 the induced
polarization curve shows a discontinuous step, but as the electric field increases, 0.07, 0.08
and so on, the polarization changes continuously from a large value at low temperature to a
relative small value at high temperature, showing a continuous step. So there is another
critical electric field somewhere in between 0.05<e<0.07, separates the discontinuous step
Theories and Methods of First Order Ferroelectric Phase Transitions

287
and the continuous step of the induced polarization. In fact, this tri-critical point would be
around e=0.06. It is also important to remark that the above-mentioned features of the field
induced phase transitions have been observed in lead magnesium niobate (Kutnjak et al.,
2006), which is a well-known ferroelectric relaxor.

Fig. 10. Temperature dependence of the field induced polarization for Ω=1.15 and g=0.8. The
parameter is the strength of the electric field. (Wang et al., 2008)
Ferroelectrics

288
For further understanding the field induced phase transitions, Fig. 11 shows the hysteresis
loops obtained numerically from Eq. (32) and corresponding to the curves displayed in Fig.
10. Double hysteresis loops can be observed when the temperature is lower than a critical
point, around t=0.6, suggesting that ferroelectricity can always be induced at very low
temperature. When the temperature is higher than this critical value, there is no hysteresis
loop and we can just observe a non-linear p–e behaviour (see for instance the case for t=0.7).
However, when the electric field is lower than e≈0.025, as indicated by the dashed arrow in
Fig. 11, no hysteresis loop can be observed. That is the case corresponding to the curves e
=0.01 and 0.02 in Fig. 10. The critical electric field able to induce a phase transition logically
increases with the increasing of temperature, so at lower temperature region in Fig. 10, we
can always have field induced ferroelectricity when the applied electric field is strong
enough.

Fig. 11. Hysteresis loops at different temperatures for Ω=1.15 and g=0.8. The dashed arrow
indicates the minimum electric field needed to induce a ferroelectric state at t=0. (Wang et
al., 2008)
To understand the influence of the zero point energy on the shape of hysteresis loop, here
we take the case of g=0.8 at t=0 as example. The corresponding quantum temperature, after
Eq. (31), is
( ) 0
Q
t t = = Ω
and then, Eq. (32) becomes

1 3
tanh e p p gp
−
= Ω − − (34)
Fig. 12 plots the hysteresis loops calculated after Eq. (34). When the zero point energy is
smaller than the critical value Ω
cf
(Ω
cf
=1.1236, in this case) a normal hysteresis loop is
obtained, where the coercive field decreases as zero point energy increases. For the critical
value, a double hysteresis loop with zero coercive field is found. But if we continue
Theories and Methods of First Order Ferroelectric Phase Transitions

289
increasing the zero point energy, we arrive to a point where no hysteresis loop is found at
all. That suggests that above this other critical value, be Ω
cp
, there is no way to induce a
phase transition, even applying a strong field, and the system remains always in a
paraelectric state.

Fig. 12. Hysteresis loops at zero temperature for different zero point energy values. The
critical value of Ω
cf
is the minimum zero point energy for the system to have ferroelectricity,
while the critical value of Ω
cp
is the maximum zero point energy for the system to get field
induced ferroelectricity. (Wang et al., 2008)
From the analysis of the hysteresis loops in Fig.12 we can determine the critical electric field
needed to induce phase transition imposing the conditions,
2
2
0, 0
c
p
e e
p p
⎛ ⎞ ⎛ ⎞ ∂ ∂
= >
⎜ ⎟ ⎜ ⎟
∂ ∂
⎝ ⎠ ⎝ ⎠

( ) ( ) ( )
2
2
3 1 3 1 6 2
6
c
g g g
p
g
− + − Ω−
= (36)
Substituting p
c
(g, Ω) obtained after Eq. (36) into Eq. (34) we can get the coercive field e
c
(p
c
)
at zero temperature. Besides, as it is showed in Fig. 12, when the zero point energy attains
its critical value Ω
cf
, the coercive field turns out to be zero, so this is another way to check
Ferroelectrics

290
the quadrupolar interaction dependence of the critical zero point energy Ω
cf
(g) as displayed
in Fig.9. It must be noted the full accordance between the two calculations.
At the second critical value of the zero point energy, Ω
cp
, the hysteresis loop becomes an
inflexion e-p curve as it can also be observed in Fig.12, so in this case both Eq. (35) must be
equal to zero, and by solving the system of equations, it results,

( )
2
3 1 3 1
,
12 6
cp cp
g g
p
g g
+ −
Ω = = (37)
The phase diagram at zero temperature is shown in Fig. 13. It displays the role of both the
quadrupolar interaction strength and the zero point energy on first order phase transitions.
On the top of this diagram we find just paraelectric state (PE), while on the bottom left it
appears only second order phase transitions (FE: 2nd order) that correspond to g < 1/3 and
Ω ≤ 1. On the bottom right (g > 1/3) there are the first order transitions (FE: 1st order) as the
critical values of the zero point energy (Ω
cf
>1) that depress the ferroelectricity grow
monotonously with g. Above the curve Ω
cf
(g) there are induced electric field phase
transitions (first order also). They are limited by another curve Ω
cp
(g) given by Eq. (37)
indicating that no phase transition can be observed when the zero point energy of the
system is greater than this value.

Fig. 13. Phase diagram of zero point energy critical value Ω
c
versus quadrupolar interaction
coefficient g at zero temperature. The second order phase transition region is denoted as
“FE:2nd order”, “FE:1st order” indicates a normal first order transition, “iFE” is the region
of induced ferroelectric phase and on the top, “PE” corresponds to the paraelectric phase.
(Wang et al., 2008)
From above calculations in the framework of effective field approach, it can be seen that a
phase transition can be induced by applying an electric field in a first order quantum
paraelectric material. There exist two critical values of the zero point energy, one is Ω
cf
that
depress ferroelectricity, and another is Ω
cp
above which it is impossible to induce any kind
Theories and Methods of First Order Ferroelectric Phase Transitions

291
of phase transition independently of the value of the electric field applied. Phase diagram is
presented to display the role of both the quadrupolar interaction strength and the zero point
energy on the phase transitions features.
4. Ising model with a four-spin interaction
Ising model in a transverse field with a four-spin interaction has been used to study the first-
order phase transition properties in many ferroelectric systems. Under the mean-field
approximation, first-order phase transition in ferroelectric thin films (Wang et al., 1996;
Jiang et al., 2005) or ferroelectric superlattices (Qu, Zhong & Zhang, 1997; Wang, Wang &
Zhong, 2002) have been systematically studied. Using the Green’s function technique, the
first-order phase transition properties in order-disorder ferroelectrics (Wang et al., 1989) and
ferroelectric thin films (Wesselinowa, 2002) have been investigated. Adopting the higher-
order approximation to the Fermi-type Green’s function, the first-order phase transition
properties have been studied in the parameter space with respect to the ratios of the
transverse field and the four-spin interaction to the two-spin interaction for ferroelectric thin
films with the uniform surface and bulk parameters (Teng & Sy,2005). These works prove
that Ising model with four-spin interaction is a successful model for studying first order
phase transition of ferroelectrics. In the following, basic formulism under mean-field
approximations and Monte Carlo simulation are presented, and the results are discussed.
4.1 Mean field approximation
The Hamiltonian of the transverse field Ising model with a four-spin interchange interaction
term is (Wang et al., 1989; Teng & Sy, 2005):

Eq.(42) can be rewritten in the same form in Eq. (26), which is obtained from effective field
approach. The equivalence of effective field approach and Ising model with four spin
couplings under mean field approximation is completely approved. Therefore the critical
value of relative quadrupolar contribution is g
c
=1/3 under mean field approximation for
occurrence of first order phase transition.
4.2 Monte Carlo simulation
A well known and useful method to study phase transitions is by means of the Monte Carlo
simulations (Binder, 1984). In particular, phase transitions in Ising systems of relatively low
dimensions are sufficient to carry out numerical simulations in the vicinity of the transition
temperature, providing a good empirical basis to investigate the asymptotic behavior at the
phase transition (Gonzalo & Wang, 2008). Here Monte Carlo simulation is applied to the
Theories and Methods of First Order Ferroelectric Phase Transitions

293
Ising model with four-spin coupling for studying the phase transition behavior, especially
checking the critical value from the four-spin coupling strength, or quadrupolar
contribution (Wang et al., 2010).
Monte Carlo method with metropolis algorithm has been used to simulate 3D Ising cubic
lattice. The Hamiltonian is same as in Eq.(38), but without the first term, i.e., without
including the tunneling term. In this case, the critical value of the four-spin coupling
contribution under mean field approximation is
( )
12 ' 2 ' 1
, '/ 1/6
3
c
c
J J
g J J
J J
= = = =

The critical four-spin coupling strength is J’/J=1/6 from mean field theory, which is a
reference value for the Monte Carlo simulations. Periodic boundary condition has been used
in the simulations. The lattice size is denoted as N=L×L×L, where L is edge length. In the
Monte Carlo simulation, edge length L=20, 30, 100 are used. Monte Carlo steps are chosen
different for different lattices size to achieve an adequate accurate of the results.

Fig. 14. Temperature dependence of spin average (a) and reduced average energy of cubic
lattice with edge length L=20 and 30 for different four-spin coupling strength J’/J. (Wang et
al., 2010)
Simulation is started with relative small lattice size, with edge length L=20 and 30. The
temperature dependence of the spin average and the reduced average energy with different
four-spin coupling strength are presented in Fig.14. The reduced average energy is defined
as the energy with respective to the ground state energy E
0
in the temperature of zero
Kelvin. The curve for lattice size L=20 is marked by solid symbols, and that for L=30 is
marked by open symbols. The temperature is in the scale of two-site coupling J. As the four-
spin coupling strength increases from J’/J =0 to J’/J =1, the transition temperature is shifted
to higher temperature. The decreasing of the average spin and the increasing of the reduced
average energy, with increasing temperature around the transition temperature becomes
more rapidly as J’/J increases. The general difference between L=20 and that of L=30 is
marginal except around the transition temperatures. Even though the four-spin coupling
Ferroelectrics

294
strength (J’/J) is much larger than that of the mean field value 1/6, the first order transition
characteristic is not such obvious in these two lattice sizes.
The temperature dependence of spin average and the reduced average energy of lattice size
100 is shown in Fig.15 for different four-spin coupling strength J’/J. The value of J’/J
increases from 0.0 to 1.1 with increment of 0.1, corresponding the curves from left to right.
The general behavior seems similar with that for L=20 and 30 as shown in Fig.14. However,
with increasing of the four-spin coupling strength J’/J, as can be seen in the most right side
curve of J’/J=1.1 in Fig.15(a), the spin average drops down around the transition
temperature very quickly, showing a discontinuous feature. Similar discontinuous feature
can be also seen in the reduced average energy curves in Fig.15(b). The reduced average
energy goes up very sharply around the transition temperature for J’/J=1.1, as shown in the
most right side curve in Fig.15(b). From Fig.15(b), we also notice that there is an inflexion
point around the transition temperatures. The reduced average energy at this point is about
1/3 of the ground state energy when J’/J is larger. This condition could supply a criterion
for determine the transition temperature in the first order phase transition.

Fig. 15. Temperature dependence of spin average (a) and reduced average energy (b) of
lattice size L =100 for with different four-spin coupling strength J’/J. (Wang et al., 2010)
To determine the transition temperature, we appeal the calculation of the Binder cumulant.
The temperature dependence of the Binder cumulant for J’/J= 1.0 with different lattice size
are shown in Fig.16. For lattice size of L=10, 20, 25, 30 and 40, the Binder cumulant does
cross the point at T
c
=8.148J. For lattice size L is larger, see L= 50, 70, 100 and 150, the Binder
cumulant misses the cross point, and drops down from 2/3 to a very small value at higher
temperatures. That means that the transition temperature can not be obtained from the
Binder cumulant when the four-spin coupling strength J’/J is larger. It is believed that the
Binder cumulants in Fig.16 suggesting the transition is of second order when the lattice size
is smaller than L=40, and the transition is of first order when the lattice size is larger than
L=40. The lattice size L=40 is around the critical lattice size for four-spin coupling strength
J’/J =1. This also implies that the transition temperature of first order transition is lattice size
dependent.
Theories and Methods of First Order Ferroelectric Phase Transitions

295

Fig. 16. Binder cumulants for J’/J= 1.0 with different lattice sizes. The circle indicates the
cross point of the Binder cumulants for lattice size L<40. (Wang et al/, 2010)

Fig. 17. Temperature dependence of spin average of lattice sizes L=100 for different J’/J
around the transition temperature. Temperature is scaled by the transition temperature
determined by the criterion <E>/E
0
=1/3. (Wang et al., 2010)
Fig.17 shows the temperature dependence of spin average and the reduced average energy
of lattice size 100 as shown in Fig.15, but with temperature rescaled by the transition
temperature T
C
. The transition temperature T
C
is determined by the criterion of the
averaged energy being one third of the ground state energy, i.e., temperature at
<E>/E
0
=1/3 being the transition temperature, as circled in Fig.17(b).
Results from Monte Carlo simulations on Ising cubic lattices with four spin couplings
suggest that, (1) critical value of four-spin coupling strength for occurrence of first order
Ferroelectrics

296
phase transition is larger than that of mean field theory; (2) the critical value is lattice
dependence. When lattice size is smaller, the phase transition is still of second order; (3)
when the phase transition is of first order, the transition temperature can be determined by
the average energy being a third of the ground state energy. However, this criterion has not
been justified rigorously.
5. Ferroelectric relaxors
Ferroelectric relaxors have been drawn much attention because of their high electro-
mechanical performance and unusual ferroelectric properties. Two review articles (Ye, 1998;
Bokov & Ye, 2006) have summarized the achievements of recent researches on ferroelectric
relaxors, especially for lead magnesium nibate (PMN). Basically, there are two categories of
explanations about the fundamental physics of their unusual properties. One is based upon
the randomness of their compositions and structures, such as Smolenskii’s theory and
spherical random bond random field model. Another is presumably based upon the
experimental phenomenon, such as macro-micro-domain and super-paraelectric model. In
this section, a general explanation of the properties observed in ferroelectric relaxors is
proposed after analysis of the later category models (Wang et al., 2009). Field induced phase
transition and diffused phase transition are reproduced within the framework of effective
field approach.
Interpretation is started with the experimental results of field induced phase transition in
PMN. The temperature dependence of the polarization under different electric field
strengths has been obtained (Ye & Schmid, 1993; Ye, 1998). From this relation we can
understand that (1) there is no ferroelectric phase transition in the whole temperature range,
since there is no spontaneous polarization as the temperature goes down to zero Kelvin; (2)
ferroelectricity can be induced by an external electric field. These imply that the phase
transition in PMN is of first order, but the ferroelectricity is depressed in the whole
temperature range. To understand these characteristics of ferroelectric relaxors, we can
recall the temperature dependence of the spontaneous polarization in a typical normal first
order ferroelectric phase transition is shown in Fig. 2. This implies that PMN is in a
paraelectric state, but not far from the ferroelectric state.
Apart from the field induced phase transition, the following features should be also found
within this temperature range in a normal first order ferroelectric phase transition: (1) a very
long relaxation time, because of the critical slow down as the temperature is near the critical
temperature. (2) super-paraelectric behavior. Normally there should be a double hysteresis
loop observed in this temperature range. However, the double hysteresis loop could be
reduced to a super-paraelectric shape because of the long relaxation time of the critical slow
down. (3) macro-micro-domain crossover. As the temperature is much lower than the
critical temperature, single domain or macro-domain is expected since it is in ferroelectric
state; as the temperature is much higher than the critical temperature, no domain will be
observed as it is in paraelectric state. Around the critical temperature, macro-micro-domain
crossover is expected, i.e., polar nano-regions are forming in this temperature range. All
these features have been observed in the ferroelectric relaxors like PMN.
The depression of the ferroelectricity in PMN reminds us of the case of quantum
paraelectrics SrTiO
3
. Therefore the field induced phase transition in a first order phase
transition depressed by quantum fluctuation has been investigated within the framework of
effective field approach by inclusive of zero point energy (Wang et al., 2008). The
Theories and Methods of First Order Ferroelectric Phase Transitions

297
temperature dependence of the induced polarization under different electric field is shown
in Fig.10. The polarization p and temperature t are in dimensionless unit, the numbers
marked in the Fig.10 are the strength of electric field.
The major difference between the temperature dependence of the polarization in PMN (Ye
& Schmid, 1993; Ye, 1998) and Fig.10 appears at lower temperature range. The polarization
of PMN is still difficult to recover by an external field. This suggests that the zero point
energy at lower temperature could be much larger than that in the higher temperature. In
other words, the zero point energy might be increased with decreasing of temperature.
Another evidence of the existence of larger zero point energy can be found from the diffused
phase transition in PMN. For the quantum temperature scale with constant zero point
energy, the temperature dependence of the dielectric constant has been obtained from
Monte Carlo simulation on a Ising model (Wang et al., 2002). As the zero point increases, the
transition temperature or the peak temperature of the dielectric constant shifts to a lower
temperature. As the zero point energy is larger than the critical value, quantum paraelectric
feature is obtained. When the zero point energy increases further, the dielectric constant
decreases at low temperature. Therefore if the zero point energy changes with temperature
and has a larger value only at lower temperature, the dielectric constant will increase as the
temperature increases at lower temperature side, and decreases as the temperature increases
at higher temperature side. A round dielectric peak will be formed around the temperature
of zero point energy dropping down.
From above analysis, a temperature dependent form of zero point energy is proposed in the
following form (Wang et al., 2009)

0
( )
1
X
T T
e
α −
ω
ω =
+
=
=
(44)
where the zero point energy ω changes around temperature T
x
from ω
0
at lower temperature
to a relative lower value with crossover rate α. By using the same technique of effective field
approach as in Refs.(Wang et al., 2008; Yuan et al., 2003 Gonzalo, 2006), with the quantum
temperature scale in Eq.(32) and the zero point energy in Eq.(44), the field induce phase
transition and diffused phase transition are obtained and shown in Fig.18. All parameters
are in dimensionless scale, e stands for the electric field, and k is for the dielectric constant.
From Fig.18 we can see that the basic features of field induce phase transition and diffused
phase transition observed in relaxor ferroelectric are reproduced.

298
The dimensionless quantum temperature scale used in Fig.18 is shown in Fig.19. The solid
line represents the quantum temperature scale, and the dashed line is for the real
temperature scale. The phase transition temperature is marked by the arrow. That means
that the state evolution of relaxor ferroelectric misses the phase transition temperature as the
temperature decreases, and re-entry of the paraelectric state. The kind of non-ergodic
behavior is schematically shown in Fig.19(b) for better understanding.

Fig. 19. (a) Quantum temperature scale and (b) non-ergodic behavior. (Wang et al., 2009)
Overall, relaxor ferroelectrics like PMN are in a tri-critical state of long range ferroelectric
order, thermal fluctuations and quantum fluctuations. This critical state can be described by
a quantum temperature scale. Following features can be understood from this issue: diffuse
phase transition, field induced phase transition, long relaxation time, as well as super-
paraelectric state, micro-macro-domain crossover and nonergodic behavior. However, a
more adequate expression of temperature dependence of zero point energy is still needed
for better description of the physical behavior in the relaxor ferroelectrics.
6. Final remarks
Theoretical methods and models for studying ferroelectric with first order phase transition
are definitely not limited to the contents in this chapter. Hopefully results from these
theoretical techniques can provide useful information for understanding experimental
observations. Heavy-computer relying methods, such as first-principle calculations and
molecular dynamic simulations etc, have been applied to investigate the physical properties
of ferroelectrics. However, fully understanding of the origin of ferroelectrics might need
more efforts from both theoretical and experimental side.
7. References
Ali, R.A.; Wang, C.L.; Yuan, M.; Wang, Y. X. & Zhong, W. L. (2004). Compositional
dependence of the Curie temperature in mixed ferroelectrics: effective field
approach. Solid State Commun., 129, 365 -367
Arago, C.; Garcia, J.; Gonzalo, J. A.; Wang, C. L.; Zhong, W. L. & Xue, X. Y. (2004).
Influence of quantum zero point energy on the ferroelectric behavior of
isomorphous systems. Ferroelectrics, 301, 113 -119
Theories and Methods of First Order Ferroelectric Phase Transitions

300
Wang, C. L.; Garcia, J.; Arago, C., Gonzalo, J. A. & Marques, M. I. (2002). Monte Carlo
simulation of quantum effects in ferroelectric phase transitions with increasing
zero-point energy, Physica A, 312, 181-186
Wang, C. L.; Li, J.C.; Zhao, M.L.; Zhang, J.L.; Zhong, W.L.; Aragó, C.; Marqués, M.I. &
Gonzalo, J.A. (2008). Electric field induced phase transition in first order
ferroelectrics with large zero point energy. Physica A, 387, 115-122
Wang, C. L.; Li, J. C.; Zhao, M. L.; Liu, J. & Zhang, J. L. (2009). Ferroelectric relaxor as a
critical state. Science in China Series E: Technological Sciences, 52, 123-126
Wang, C. L.; Li, J.C.; Zhao, M. L.; Marqués, M.I.; Aragó, C. & Gonzalo, J. A. (2010). Monte
Carlo simulation of first order phase transitions, Ferroelectrics, (in press)
Wang, X. S.; Wang, C. L. & Zhong, W. L. (2002). First-order phase transition in ferroelectric
superlattice described by the transverse Ising model. Solid State Commun. 122, 311-
315
Wang, Y. G.; Zhong, W. L. & Zhang, P. L. (1996). Surface effects and size effects on
ferroelectrics with a first-order phase transition. Phys. Rev. B, 53, 11439-11443
Wesselinowa, J. M. (2002). Properties of ferroelectric thin films with a first order phase
transitions. Solid State Commun., 121, 89-92
Ye, Z. G. & Schmid, H. (1993). Optical, Dielectric and Polarization Studies of the Electric
Field-Induced Phase Transition in Pb(Mg
1/3
Nb
2/3
)O
3
[PMN] Ferroelectrics, 145, 83-
108
Ye, Z. G. (1998). Relaxor Ferroelectric Complex Perovskites: Structure, Properties and Phase
Transition, Key Engineering Materials, 155-156, 81-122
Yuan, M.; Wang, C. L.; Wang, Y. X.; Ali, R. A. & Zhang, J. L. (2003). Effect of zero-point
energy on the dielectric behavior of strontium titanate. Solid State Commun., 127,
419-421
17
Electroacoustic Waves in a Ferroelectric Crystal
with of a Moving System of Domain Walls
Vilkov E.A. and Maryshev S.N.
1
Kotel'nikov Institute of Radio Engineering and
Electronics of Russian Academy of Sciences, Ul'yanovsk Branch,
2
Moscow Institute of Physics and Technology
Russia
1. Introduction
In addition to conventional applications of ferroelectric crystals that exhibit piezoactivity,
such crystals find wide application in the production of domain electronic devices based on
the interaction between acoustic waves and ferroelectric domains (acousto-domain
interaction) [Esayan et al, 1974]. In the course of the general development of technology of
phonon crystals the ferroelectric with periodic domain structures (PDSs) have attracted a
considerable interest recently [Golenishchev-Kutuzov et al, 2003]. The interest in such
structures with periodically varying elastic, electric, and other physical parameters dates
back to the 1960s since, by that time, the possibilities offered by single-domain crystals in the
realization of the spectral characteristics of elastic and electromagnetic waves had been
exhausted. First of all a ferroelectrics with PDSs differ from usual phonon crystals by ability
of its reorganization under external action due to rather fast moving domain walls(DW)
[Golenishchev-Kutuzov et al, 2003].
The spectra of elastic oscillations of a ferroelectric with a static PDS may significantly differ
from the spectra of a conventional single-domain sample [Li, et al, 1991; Lyubimov &
Sannikov, 1979]. This difference is primarily manifested in the formation of forbidden and
allowed bands, which are absent in the continuous spectrum of waves in a single-domain
crystal. To the full this conclusion extends to oscillation modes of localized at DWs, in
particular – to electroacoustic interfacial waves (EIWs) [Maerfield & Tournois, 1971], which
were widely studied in ferroelectrics with static PDSs, representing a superlattice [Li, et al,
1991; Nougaoui, 1987]. Considerable modification of spectral parameters of EIWs in
superlattices such as boundary localization of oscillation and phase speed was explained in
[Lyubimov & Sannikov, 1979; Li, 1987] as result of interaction between electrosound
oscillations of neighbo(u)ring DW.
At an early stage of research the possibility of the realization of PDSs with various periods
of the lattices of domain walls and the possibility of vary lattice period [Golenishchev-
Kutuzov et al, 2003] have shown the prospects of application of the domain superlattices. It
was found out, in particular, that crystals with PDSs are effective as broadband
piezoconverters of acoustic waves, and with the greater efficiency of transformation, than
have monodomain crystals [Batanova & Golenishchev-Kutuzov, 1997]. Other fields of
application (the acoustic spectroscopy of polydomain ferroelectrics and processing of the
Ferroelectrics

302
signal information) have demanded of studying of effects of a refraction of acoustic waves
from packages of DWs of ferroelectrics. So, in development of results of work [Esayan et al,
1974] it has been shown, that appropriate variations in the period of the domain lattice,
crystal parameters, and conditions of wave propagation make it possible to control the
height, number, and location of Bragg reflections peaks [Shuvalov & Gorkunova, 1999;
Shenderov,1997], thus providing prospects for various applications.
All the results listed above are related to the static case, i.e. they are obtained for domain
lattices with motionless DW. It means that the manipulation of PDSs expressed by moving
DWs occurs not during the process of acousto-domain interaction. The overlap of the
procedure of adjustment PDSs and the process of acousto-domain interaction is interesting
due to a number of circumstances.
First, this overlap demands modeling of a supernumerary situation of work of the acousto-
domain device at "failure" of device domain structure. Second, it is necessary for research of
additional opportunities, for example, scanning of a crystal by means of EIWs on moving
DW [Gulyaev et al, 2000] or realization of ideas put forward by Auld [Auld,1973] of the
Doppler transformation of a spectrum of frequencies of bulk acoustic waves refracted by
moving DW [Shevyakhov, 1990]. Thus, it is expedient to generalize the results of the
research of acoustic properties of static superlattices of ferroelectric to the case of dynamic
superlattices whose distinctive feature is adjustable moving domain boundaries. Below, on
the basis of our works [Vilkov, 2008; Vilkov, 2009; Vilkov et al, 2009] the propagation of
guided EIWs and bulk electrosound waves in a dynamic superlattice of equidistant
uniformly moving 180-degree DW is considered. Let's notice, that until now the research of
acoustic effects in crystals of ferroelectrics with moving DW was limited to cases of non-
collective acousto-domain interactions:a single DW [Shevyakhov, 1990; Gulyaev et al, 2000],
a strip domain (i.e., a pair of DWs) [El’meshkin & Shevyakhov, 2006] and a structure of a
two adjacent strip domains [Bugaev et al, 2005].
2. Basic equations for a shear wave in ferroelectric in the frame of the DW at
rest
In acoustoelectronics, the elastic deformation and electric-field intensity E
j
normally serve
as independent quantities that determine the state of a piezoactive ferroelectric medium.
The elastic deformation is determined by the deformation tensor

Fig. 1. The geometry of the propagation of a shift wave of horizontal polarization
For final writing of the equations (8) we consider, that the piezoelectric modulus changes
the sign in the neighboring domains divided by 180-degree DWs because of the antiparallel
orientation of the polar directions, i.e. the plane of wave propagation

( ) 1
15 15
1 , 0
j j
e e e
+
= − > ( ) . (9)
where j= 1 and 2 stand for domains of the “+” and “–” types with positive and negative
piezoelectric moduli, respectively. As a result we write down of the equation (8) in the form of

305
where ∇
2
=(∂
2
/∂x
2
+∂
2
/∂y
2
) is the Laplace operator, and shift displacement u
z
have designated
as u
j
according number of domain j.
Domain walls can move in ferroelectrics under specific external actions. In this case, to
construct a solution in domains, it is necessary to consider the equation (10) in the frame of
the DW at rest 0 x yz

by
piezopolarization charges [Lyubimov & Sannikov, 1979].
3. The electroacoustic bulk propagating waves in a ferroelectric with a
system of moving periodic domain structure
3.1 The statement of the problem
In this section we consider the influence of a uniform motion of domain boundaries forming
a dynamic superlattice of the tetragonal ferroelectric, on spectral properties of bulk
electrosound waves (EW). The comparison of the phonon spectra of static and dynamic
superlattices allows a more detailed description of specific wave processes realized in
periodic structures. The results obtained indicate that even slow DW motions cause
significant (detectable) variations in the wave spectra.
The schematic of the problem is presented in Fig. 2. We assume that, in a crystallographic
system with the fourth-order symmetry axis that is parallel to the z axis of laboratory frame
xOyz , a 4mm ferroelectric represents a superlattice of 180-degree DWs with period 2d (d>>Δ
is the distance between neighboring DWs and Δ is the DW thickness). The superlattice
uniformly moves at the velocity V
D
⎜⎜ y [010]⎜⎜. Positive velocity V
D
corresponds to the
superlattice motion codirectional with the y axis. To eliminate the significant structural
sensitivity of DWs to the regime of motion related to the generation of both spontaneous
polarization and spontaneous deformation in domains [Sosnin. & Strukov, 1970; Vainshtein,
Ferroelectrics

306
1988], we restrict the consideration to subsonic DW velocities. We also assume that the
ferroelectric is far from the phase transition. Then, the DW motion is realized at V
D
= const
and the current coordinates are given by y
n
=V
D
t+nd, where t is time; n=0, ±1, ±2,… and
DWs are geometrically thin and structureless objects (kΔ << 1, where k is the EW wave
number).

Fig. 2. Schematic representation of a domain superlattice with an electroacoustic eigenwave.
The dashed lines indicate that two elementary cells are reproduced in the positive and
negative directions of the Y axis and form an infinite superlattice. Vectors k’ and k’’show
the direction of the EW propagation. The arrow shows the direction of the lattice motion.
Here, Е
0
is the electric-field intensity in domains
It is known [Vainshtein, 1988] that the above conditions are valid for DWs in BaTiO
3
-type
ferroelectrics at ultrasonic frequencies. It is commonly accepted [Maerfield & Tournois, 1971;
Auld,1973] that, in this case, the ferroelectric can be considered as a piezoelectric crystal that
is periodically twinned with respect to the planes y = y
n
. With regard to the analysis of
propagation of only horizontally polarized shear waves in the (001) crystal plane, we
assume that antiparallel polarizations in the neighboring domains are related to the sign
alternation of the piezoelectric modulus according equation (9). At that, there are in eq.(9)
j = 1 for (n-1)d + V
D
t < y< nd+ V
D
t and j = 2 for nd + V
D
t< y <(n+1)d+ V
D
t (n = 0, ±2, ±4,…).
The remaining characteristics of domains are identical.
Then, we assume that the electroacoustic eigenwaves with the wave vector = k’=(k’sinθ’,
k’cosθ’, 0) propagate in the XOY plane at angle θ’ relative to the normal to the plane of 180-
degree DWs in the positive direction of the y axis (Fig. 2). For the electroacoustic eigenwaves
propagating in the XOY plane at angle θ" to the normal to the DW plane in the negative
direction of the y axis, we employ another wave vector, = k’’=(k’’sinθ’’, k’’cosθ’’, 0) in
accordance with another expected Doppler shift [Shevyakhov, 1990].
Electroacoustic Waves in a Ferroelectric Crystal with of a Moving System of Domain Walls

307
The system of equations for these waves in the neighboring domains with numbers j = 1 and
2, which results from the reduction of Eqs. (3) and (4) in accordance with the cyclic Bloch
conditions in the case of 180-degree DWs, is represented by equations (9),(13), (14). The
fields on the moving DWs of the lattice exhibit the phase conjugation for the wave
characteristics of EWs that travel in the direction opposite to that of the DW propagation.
Hence, the following relationships are valid [Shevyakhov, 1990]:

' ' ''
' ' 2 2
' ' ' '
' ' 2 2 2 2
2 2( / )
cos (1 / ) 2 /
cos , .
1 / 1 2( / ) cos /
y D
D D
y y
D D D
k V v k
V v V v
k k
V v V v V v
θ
θ
θ
+
+ +
= = − +
− + +
(15)
Here, ν is the EW phase velocity in a single-domain crystal. In the case of a static lattice
(V
D
=0), the wave characteristics of the oppositely directed eigenwaves are identical:
θ = θ’’ = θ’,
'' '
y y y
k k k = = .
To ensure the interaction between an EW with wave vector k’ and a DW moving away, we
must provide for faster (in the signal meaning) wave propagation relative to the DW. In
accordance with [Shevyakhov, 1990], this can be realized through imposition of a limitation
on propagation angle θ’, θ’ < θ**. Owing to the coincidence of the phase and group velocities
of an EW in a singledomain crystal, the critical angle θ** = arcos(-V
D
/ν) determines the
equality of the projection of the EW group velocity on the direction of the DW motion and
the DW velocity.
When θ’ > θ**, , the DW motion along the direction of the DW displacement is faster than
the motion of any plane train of EWs with the same angle of incidence θ’. From the physical
point of view, this situation corresponds to the vanishing acousto-domain interaction. In
addition to the condition θ’ < θ**, we assume that the EW wavelength is significantly smaller
than the crystal dimension. Under such conditions, the boundary effects at the outer
interfaces of the ferroelectric and its shape weakly affect the behavior of waves and, hence,
can be disregarded.
3.2 Dispersion equation
We assume that the domains with numbers 1 and 2 are located between the DWs with the
coordinates y

= 0, d, 2d (Fig. 2). We search for the solution to Eqs. (13) in the region of the
first domain in the following representation:

(17)
To join the domain fields in the frame of the DW at rest on the interface y d =

in the
nonrelativistic quasistatic approximation, we employ the conventional continuity
conditions [Auld, 1973] for shear displacements; potentials; the shear components of the
stress tensor,
Ferroelectrics

308

44
j j
j j
yz
u
T c e
y y
ϕ ∂ ∂
= −
∂ ∂
( ) ( )

(18)
and the y components of the electric induction,

1
4 .
j j
j j
y
u
D e
y y
ϕ
ε π
∂ ∂
= −
∂ ∂
( ) ( )

(19)
Thus, with allowance for expressions (14), (18), and (19), we obtain the following boundary
conditions:

where the values of the fields u
1,2
, α
1,2
, ϕ
1,2
, and σ
1,2
on the right-hand side of the identities
for the subscript j = 1 correspond to 0 y =

and the plus sign is selected. For the subscript j =
2, we use the field values at y d =

and choose the minus sign. In expressions (22), we
introduce quantity
2 2 *
15 1 44
4 / e c Κ π ε = , which is the squared coefficient of the
electromechanical coupling of the crystal for the shear waves that propagate in the (001)
basis plane. For brevity, we use the following notation in expressions (22):
Electroacoustic Waves in a Ferroelectric Crystal with of a Moving System of Domain Walls

with allowance for expression
(15).
We represent the fields in the domain with the subscript j = 1 on the DW 0 y =

in terms of
their values at arbitrary point y

of the given layer. For the domain with the subscript j = 2,
we represent the fields on the DW y d =

in terms of their values at an arbitrary point of this
layer. For this purpose, we find matrices that are inverses of the 4 ×4 square matrices
consisting of the coefficients of u
1,2
, α
1,2
, ϕ
1,2
and σ
1,2
in expression (18). At y d =

1 2
cos(2 ) cos(2 ). cos(2 ) ch(2 ).
y x
d k d d k d κ κ = = , (28)
For the case under study, this factorization of Eq. (25) corresponds to the extinction of the
interaction between acoustic and electric oscillations that is due to the absence of the
piezoelectric effect (K = 0) or the absence of near-boundary electric oscillations in the
domains Φ
j
= 0 [Shuvalov & Gorkunova,1999] under the conditions for the EAW normal
propagation (k
x
= 0) when the acousto-domain interaction vanishes. A similar result is valid
for Eq. (20), which can be represented also as a product of the dispersion relations for
independent elastic and electric subsystems.
For the case under study, this factorization of Eq. (25) corresponds to the extinction of the
interaction between acoustic and electric oscillations that is due to the absence of the
piezoelectric effect (K = 0) or the absence of near-boundary electric oscillations in the
domains Φ
j
= 0 [Shevyakhov, 1990] under the conditions for the EW normal propagation
(k
x
= 0) when the acousto-domain interaction vanishes. A similar result is valid for Eq. (24),
which can be represented also as a product of the dispersion relations for independent
elastic and electric subsystems.
When k
x
=0 or K = 0, the first equation from (28) becomes identity, a result that means that a
purely elastic wave
1
propagates in the crystal along the normal to the domain planes with
propagation constant k
y
(i.e., a bulk shear wave is excited in an infinite crystal). It follows
from the second identity that the Bloch number is either purely imaginary (K = 0), i.e., a
solution does not exist, owing to the formation of a continuous forbidden band) or (k
x
=0)
equal to 2πn / (2d), where n is integer. In the second case (k
x
=0), the boundary conditions are
satisfied if A
1
= 0, B
1
= 0, A
2
= 0, B
2
= 0, and B
2
= 0 (i.e., all of the fields are identically zero).
Therefore, the solution is degenerate and must be disregarded. Excluding both variants
(k
x
= 0 and K = 0) as the variants that do not allow the acousto-domain interaction, we
assume that Eq. (24) always describes coupled electroacoustic oscillations for a static
superlattice.

1
At K ≠0, this wave is accompanied by the in-phase oscillations of the electric field (see the first term in
expression (14)).
Ferroelectrics

312
3.3 Solution and analysis of the dispersion equation
A numerical solution to Eq. (24) that has been obtained with the use of expression (27) is
shown in Fig. 3. In this study, the calculations are performed for a barium titanate crystal
((BaTiO
3
) with the following parameters: the crystal density ρ= 5 g/cm
3
, K
2
≈ 0.37, the
velocity of the transverse waves in the absence of the polarizing field c
t0
= (c
44
/ ρ)
1/2
= 2×10
5

cm/s, ε
1
= 5×10
3
, and e
15
≈ 3⋅10
6
g/(cm s). Figures 3a and 3b respectively demonstrate the
real and imaginary parts of the roots of the dispersion equation for the static (dashed lines)
and moving (solid lines) superlattices. The results are obtained for the propagation angle
θ’’ = π/3 and the positive direction of DW motion (V
D
> 0). The numbers of the curves
correspond to the root numbers (λ
1
, λ
2
, λ
3
, λ
4
). The roots λ
1,2
= exp(2iκ
1,2
d) in expression (27)
(Fig. 3a, curves 1, 2) are purely real. This means that the Bloch wave numbers κ
1,2
are purely
imaginary for any wave number k and correspond to the modes that are forbidden for the
given periodic structure. Note that the shapes of curves 1 and 2 remain almost unchanged
when the motion is taken into account. The roots λ
3,4
= exp(2iκ
3,4
d) (Fig. 3a, curves 3, 4)
describe propagating waves. Below, we consider only the spectral properties of the
propagating eigenmodes of the superlattice.

0 1 2 3
-1
0
1
2
Re(e
2iκd
)
(k
"
y
d) / π
1
2
3
4
'
3
'
4

Fig. 3. (a) Real parts of the roots λ
1
, λ
2
, λ
3
(3, 3’), and λ
4
(4, 4’) and plotted as a function of
(
y
k′′ d)/π for various values of V
D
: (1, 2, 3', 4') 0 and (3, 4) 0.01v. Curves 3' and 4' coincide
except in the region of the loop-shaped segments, (b) Imaginary parts of the roots λ
3
(3, 3’),
and λ
4
(4, 4’) plotted as a function of (
y
k′′ d)/π for various values of V
D
: (3, 4) 0.01 v, 3’, 4’
It is seen from Fig. 3a that, in the static case, the real parts of roots 3 and 4 are cosines whose
arguments contain the Bloch number. The imaginary parts of these roots are the sines of the
above argument. It follows from the comparison of Figs. 3a and 3b that curves 3 and 4
describe counterpropagating waves. Indeed, the spectral characteristics of the modes of the
static superlattice that propagate in the opposite directions must differ only by the sign of
the Bloch wave number: The positive and negative Bloch wave numbers respectively
correspond to the waves that propagate in the positive and negative direction of the y

axis.
Electroacoustic Waves in a Ferroelectric Crystal with of a Moving System of Domain Walls

313
The calculations show that an increase in propagation angle θ'' leads to an increase in the
width of the loop fragment (Fig. 3) on the curve of the real part of the root. In accordance with
Fig. 3b, the imaginary part of the root is absent for this spectral interval in the case of the
dashed curves. Thus, the Bloch wave number, which is the propagation constant averaged
over the lattice period, is purely imaginary and the wave propagation is impossible, so that the
corresponding fragment is a forbidden band [Balakirev & Gilinskii, 1982].
The appearance of forbidden bands is obvious. In accordance with Fig. 3a, the Bloch vector
exhibits variations in the transmission band, so that an integer number of half eigenwaves is
realized at the band edges. At each boundary, this circumstance corresponds to the in phase
summation of the forward wave and the wave that is reflected from the edge whose
distance from the boundary equals the period of the structure. In contrast, the forward and
reflected (antiphase) waves are mutually cancelled in the band gaps.
An increase in angle θ'' results in a simultaneous increase in the widths of allowed and
forbidden bands. However, their number decreases in the range of wave vectors 0 < k'' < 2
×10
5
cm
-1
(the frequency range 0 < ω'' < 5 ×10
10
s
–1
), which is common to all of the plots. For
the given domain size d = 10
-4
cm, dimensionless parameter kd ranges from 0 to 20. Thus, the
calculations are performed almost in the absence of limitations on this parameter.
In addition, it is seen from Fig. 3 that the DW motion causes the Doppler shift of
eigenwaves, which eliminates the degeneration of the roots of the dispersion relation. This
fact is manifested in the graphs: The real parts of roots λ
3
, and λ
4
for the counterpropagating
EWs are not equal and are described by different curves. Curve 4 corresponds to the wave
that propagates in the direction opposite to the y

axis, and curve 3 corresponds to the wave
that propagates along the y

axis. In accordance with Fig. 2, at V
D
> 0, , the forbidden bands
exhibit a shift to the long-wavelength region. The comparison with the calculated results
obtained for V
D
< 0 shows that, relative to the forbidden band at V
D
= 0, the forbidden
bands are symmetrically shifted to the shortwavelength region.
For relatively large (κ
3,4
d)/π, we observe a larger difference between curves 3 and 4. This
means that, as the number of the oscillation mode increases, the effect of the DW motion on
the EW spectrum strengthens. This result is in agreement with the results from [Vilkov,
2007], where the spectral properties of magnetostatic waves are analyzed with allowance for
the motion of a DW superlattice. In the spectral fragments with0 V
D
≠ 0 (Fig. 3) that coincide
with the spectral forbidden band of the static superlattice, a shifted forbidden band is
formed. Thus, the amplitudes of eigenwaves in this band of the moving superlattice contain
oscillating factors. In addition, new forbidden bands emerge at V
D
≠ 0 in the spectral
fragments where the real and imaginary parts of the roots of the dispersion equation are
greater than unity. This circumstance is due to the fact that the lattice motion results in an
additional phase shift between the counterpropagating waves.
The calculated results show that, if the Bloch wave number in the first spectral band in Fig. 3
is approximately equal to
''
y
k at small angles θ'', a significant difference between κ and
''
y
k
can be realized at large angles. For example, at θ = 80°, the propagation constant κ averaged
over the superlattice period is approximately two times greater than
''
y
k , a result that
indicates a significant effect of the superlattice on the spectrum of bulk EWs. The lattice
motion leads to a difference between the Bloch wave numbers of the counter propagating
waves and, hence, to differences between the EW propagation velocities and between the
field profiles that characterize EWs. Thus, the mutual nonreciprocity of the EW propagation
induced by the lattice motion needs further analysis.
Ferroelectrics

314
3.4 Calculation of the EW displacement profiles and phase
To calculate the EAW displacement profiles, we employ the periodicity condition from [Bass
et al, 1989]: On the boundaries with the coordinates 0 y =

Fig. 4. (a) Real imaginary parts of the amplitude profile of the EW shear displacement for
the wave k vector = 131300 cm–1 corresponding to the allowed band, θ’’ = 60°, and V
D
=
(dashed lines) 0 and (3, 4) 0.01v, (b) Imaginary parts of the amplitude profile of the EW
shear displacement for the wave k vector = 131300 cm–1 corresponding to the allowed band,
θ’’=60°, and V
D
= (dashed lines) 0 and (3, 4) 0.01v
Assuming that one of the amplitudes (e.g., A
1
) equals unity, we solve seven of eight
equations and represent all of the amplitudes in terms of the selected one. Then, we
substitute the resulting expressions into formulas (16) and (17) and, with allowance for the
solutions to Eq. (25), find the desired field profiles within the lattice period 0 < y

< 2d.
Figure 3 demonstrates the real and imaginary parts of the shear wave displacement in the
crystal with the static (dashed curves) and moving (solid curves) superlattices for the
positive motion of the lattice (V
D
>0). Figure 4 corresponds to the wave vector falling in the
EW spectral band in Fig. 3. It is seen that the real and imaginary parts of the displacement
respectively correspond to the symmetric and antisymmetric modes. Note that the
presented set of mode profiles is universal for given k'' and the sum of the lattice spatial
harmonics,
Electroacoustic Waves in a Ferroelectric Crystal with of a Moving System of Domain Walls

315

2
( ) exp
n
n
n
u y u i y
d
π
κ
∞
=−∞
⎡ ⎤
⎛ ⎞
= +
⎢ ⎥ ⎜ ⎟
⎝ ⎠
⎣ ⎦
∑

. (30)
This circumstance is obvious because, in accordance with expression (30), physically
nonequivalent states in the periodic structure correspond only to the range - π/d < κ < π/d.
It is seen from Fig. 4 that the amplitudes of counterpropagating waves coincide for the static
lattice and significantly differ for the moving lattice. In particular, the amplitude of the wave
propagating along the axis (curve 3) is approximately two times smaller than the amplitude
of the wave propagating in the opposite direction (curve 4). This amplitude imbalance of the
counterpropagating waves added to the misphasing can be interpreted via a variation
produced in the wave energy owing to an external source that provides for the DW motion.
The mechanism that controls the amplitude variations involves the Doppler frequency
shifts: The wave with the maximum Doppler shift (Fig. 4, curve 3) exhibits the largest
amplitude difference relative to the wave of the static superlattice (Fig. 4, dashed line). In
contrast, note minor variations in the amplitude of the wave (Fig. 4, curve 4) whose spectral
characteristics other than κare initially identical to the spectral characteristics of the wave in
the static lattice.
Each of the harmonics in expression (30) is characterized by the same displacement profile,
whereas the phase velocities are different [Balakirev & Gilinskii, 1982]:

It follows from expression (31) that, for the nth harmonic, the
phase velocity can be infinitesimal. For certainty, we set the phase velocity of the Bloch
wave in the following way:
'' ''
0
| || |,
f f
v v =

and
' '
0
| || |
f f
v v =

. The dependences of the phase
velocities of the Bloch waves on propagation angle θ'' calculated for V
D
> 0are presented in
Fig. 5.
We do not consider the limiting angles θ’’ = 0°, and θ’’ = 90°and the nearest vicinities for the
following reasons. In the first case (θ’’ = 0°), the electric-field retardation must be taken into
account in the correct analysis of the acousto-domain interaction [Balakirev & Gilinskii,
1982]. For a moving PDS, the transition θ'' → 90° is impossible because of the limitation
θ’ < θ** related to the termination of the acousto-domain interaction. It is seen from Fig. 5
that the greatest difference (about 2%) between phase velocities
'
| |
fn
v

and
''
| |
fn
v

is realized
in the interval 60° < θ < 70° and can be experimentally detected. The phase-velocity
nonreciprocity can be caused by the Doppler separation of the frequencies of
counterpropagating waves and a simultaneous variation in the Bloch wave numbers that is
due to different spatial–temporal periodicities in two opposite directions induced by the
uniformly moving DW superlattice.
4. Reflection of electroacoustic waves from a system of moving domain walls
in a ferroelectric
4.1 The statement of the problem
In the previous section we have shown, that significant modification of the spectrum of
modes of shear waves are possible owing to motion of boundaries of a superlattice of a
ferroelectric. It can be assumed, that motion of domain boundaries will exert the strong
influence on reflection of electroacoustic waves from a lattice of domain boundaries. The
important controlling role of the velocity of domain-wall motion is indirectly confirmed by
the results obtained in [Shevyakhov, 1990], which indicate that the interaction of a bulk
electroacoustic wave with a single moving domain wall in the case of a noticeable change in
the amplitude coefficients (the range where the angles of incidence are not very small) is
accompanied by the Doppler frequency transformation. By analogy with the static case
[Shuvalov & Gorkunova, 1999], it can be expected that, for a system of moving domain
walls, the reflection can be considerably enhanced in the direction of Bragg angles. At the
same time, the velocity of domain-wall motion will serves as a new parameter that is
convenient for controlling the reflection and transmission of waves in combination with
their frequency shifts. In this section the interaction of electroacoustic waves with a periodic
domain structure formed in a tetragonal ferroelectric by a finite number of uniformly
moving 180-degree domain walls is considered in the quasi-static approximation.
The schematic diagram of the problem is depicted in Fig. 6. We consider the same the
ferroelectric and the same the periodic structure, as in the previous section, but at that
periodic structure is formed by finite number 180-degree domain boundaries. It is assumed
that, in the y direction, the domain-wall lattice, which consists of 2N domains for the
structure “+–” (Fig. 6a) or 2N+ 1 domains for the structure “++” (Fig. 6b), has a period 2d, so
that d >> Δ (where d is the distance between neighboring domain walls and Δ is the
domain-wall thickness). On both sides, the lattice uniformly moving at the velocity V
D

⎜⎜y⎜⎜[010] is surrounded by semi-infinite single-domain crystal regions (the external
numbers (with respect to the lattice) of domains are n= 0 and 2N+ 1 for the structure “+–”
and n= 0 and 2N+ 2 for the structure “++”). In order to avoid a significant structural
Electroacoustic Waves in a Ferroelectric Crystal with of a Moving System of Domain Walls

317
sensitivity of domain walls to the motion regime, we will restrict our consideration to the
velocities, we will restrict our consideration to the velocity of shear waves in a single-
domain sample [Sosnin. & Strukov 1970; Vainshtein,1988]. Under the above conditions, the
motion of domain walls can be considered to be specified (V
D
= const ) with the current
coordinates y
m
= V
D
t + md, , where t is the time and m = 0, ±1, ±2,…. Correspondingly, the
domain walls are assumed to be geometrically thin and structureless (kΔ<<1, where k is the
wave number of the electroacoustic wave).

(a) (b)
Fig. 6. (a) Schematic diagram of the problem: a moving domain lattice is surrounded by
semi-infinite single-domain crystal regions with (a) opposite (structure “+–”)directions of
polarization. Tilted vectors indicate the direction of propagation of the electroacoustic wave.
The arrow indicates the direction of the lattice motion, (b) Schematic diagram of the
problem: a moving domain lattice is surrounded by semi-infinite single-domain crystal
regions with identical (structure “++”) directions of polarization. Tilted vectors indicate the
direction of propagation of the electroacoustic wave. The arrow indicates the direction of the
lattice motion
We assume, that j= 1 and 2 stand for domains of the “+” and “–” types with positive and
negative piezoelectric moduli, respectively according Eq(9). Other differences between
domains are absent. We also assume that the domain with the number n= 0 is a domain of
the “–” type for the structure “+–” and a domain of the “+” type for the structure “++” and
that the domain with the number n= 2N+ 1 or n= 2N+ 2 is a domain of the “+” type (Fig. 6).
Moreover, it also is assumed that the electroacoustic wave with the wave
k’’ = (k’’sinθ’’, k’’cosθ’’, 0), propagates in the x0y plane and is incident on the domain lattice
at the angle θ’’ (θ’’ ≠ 0). In view of the expected Doppler frequency shift [Shevyakhov, 1990],
another wave vector k’ = (k’sinθ’, k’cosθ’, 0) is assigned to reflected waves (Fig. 6). The initial
equations remain without changes and to be defined by the equations (9), (13), (14). As a
result of the phase conjugation of the fields at moving domain walls of the lattice, the wave
characteristics of the reflected and transmitted electroacoustic waves are related by the
expressions (15).
In order to avoid the analysis of the additional refraction scheme when the reflected wave
becomes adjusting with respect to the incident wave, it is necessary to introduce the
constraint on the angle of incidence θ’’ < θ* [Shevyakhov, 1990], where

2
arccos[ 2 ( / ) /(1 ( / ) )].
D D
V v V v θ
∗
= − + (32)
4.2 Technique for calculating the transmittance and reflectance of electroacoustic
waves
In the domain with the number n = 2N + 1 for the structure “+–” or with the number n = 2N
+ 2 for the structure “++,” we have the incident and reflected electroacoustic waves and the
Ferroelectrics

318
electric field wave localized at the boundary y

= 2Nd or y

= 2Nd + d (Fig. 6). The shear
displacements and the potentials of these waves as the solutions to Eqs. (13) can be written
in the form

, (33)
where the amplitude of the incident wave is taken to be unity, R is the reflectance, and C is
the amplitude of the electric wave potential. Correspondingly, for the domain with the
number n = 0 for both structures, we obtain

. (34)
Here, W is the transmittance of the electroacoustic wave and D is the amplitude of the
localized electric field wave. The solutions to Eqs. (13) in the region within the lattice for a
domain of the “+” type are sought in the following form:

, (36)
In order to match the fields of the domains in the rest system at the domain walls, in the
quasi-static nonrelativistic approximation, we use the standard requirements for the
continuity of the shear displacements, the potentials, the shear components of the stress
tensor, and the electric induction components y (see Eqs(20)). At the same time, The matrices
M
1
= M
1
(d) and M
2
= M
2
(d) (see Eqs.(23)) relate the fields at the initial and final points of the
same domain layer. Their product determines the transition matrix at the period of the
structure M = M
1⋅
M
2
.
Let us assume that, in expressions (20) and (22), the quantities determining the entire set of
waves in the domain are designated as u
0
, α
0
, ϕ
0
, and σ
0
in the domain with the number n =
0. Then, their relation to the quantities u
2N
, α
2N
, ϕ
2N
, and σ
2N
in the domain with the number
n = 2N in the structure “+–” can be found using the 4-by-4 transformation matrix M at the
period of the structure as follows:

319
relation of the fields of the domain with the number n = 0 to the fields of the last domain in
the lattice will be somewhat different as a result of the additional transformation of the
waves by the last domain; that is,

= 2Nd + d). Then, we multiply the obtained
identities by M
N
(M
N
M
2
) from the left and right and, with the use of relationships (20)-(22),
(33), (34), (37), and (38), find the systems of four equations for determining the reflectance
and transmittance: for the structure “+–,”

320
numerical calculations of the reflectance from the system of equations (40) in the case of the
static lattice are in complete agreement with those obtained in [Shuvalov &. Gorkunova,
1999]. In particular, in the short-wavelength range, the value of |R| determined from the
approximate formula (41) agrees well with the result of the exact numerical calculations.
Since the number of peaks (the main peak plus secondary peaks) in one band gap is equal to
the number of domains in the lattice, in our work, the modification of the spectrum due to
the domain-wall motion was demonstrated using small numbers N in order to provide the
clearness of the results.
The dependences of the magnitude of the reflectance of electroacoustic waves on the
reduced normal component of the wave vector at the fixed angle of incidence (θ’’ = 30°) for
the structures “++” and “+–” are plotted in Figs. 7 and 8, respectively. The calculated data
presented in these and subsequent figures were obtained for the equidistant lattice of
domains with d = 10
–4
cm in the barium titanate crystal BaTiO
3
with the following
parameters: the density of the crystal is ρ = 5 gr/sm
3
, K
2
≈ 0.37, the velocity of transverse
waves in the absence of piezoelectric effect is v = (c
44
/ ρ)
1/2
= 2⋅10
5
cm/s. In Figs. 7 and 8,
the dashed lines show the dependences ⎜R⎜
''
(2 / )
y
k d π for the static lattice according to the
calculations from the system of equations (40). The thick lines in Figs. 7 and 8 depict the
dependences ⎜R⎜
''
(2 / )
y
k d π for the lattice moving away (the direction of domain-wall
motion is opposite to the direction of the Y axis, V
D
< 0). It can be seen that the domain-wall
motion noticeably modifies the reflectance spectrum of electroacoustic waves: all peaks in
the spectrum are broadened, increase in the intensity, and are shifted toward the short-
wavelength range. In this case, the larger the ratio
''
(2 / )
y
k d π , the larger the shift, so that the
maximum of the magnitude of the reflectance can give way to its minimum.
It can be seen from the behavior of the thin lines in Figs. 7 and 8 that, in the case of the
approaching lattice (the direction of domain wall motion coincides with the direction of the
Y axis, V
D
> 0), the changes in the spectrum are as follows: the peaks in the reflectance
spectrum are narrowed, decrease in the intensity, and are shifted toward the long-
wavelength range. In this case, the larger the ratio
''
(2 / )
y
k d π , the larger the shift.
Furthermore, it was revealed that the higher the velocity V
D
, the stronger the manifestation
of the above changes in the spectrum. This effect of the shift in the spectra for the moving
lattice (V
D
< 0, V
D
> 0) with respect to the spectrum of the static lattice is explained by the
Doppler shift in the frequency of the electroacoustic wave due to its interaction with the
moving domain walls and, in actual fact, represents an analog of Mandelstam –Brillouin
scattering [Fabelinskii, 1968].It can be seen from Figs. 3,8 and Fig.3a that, when the wave
number corresponds to the band gap of the Bloch spectrum, the magnitude of the
reflectance reaches a maximum; i.e., there appears a Bragg peak. The condition for the
appearance of this peak is a correlated reflection of electroacoustic waves from all domain
walls in the lattice.
A comparison of the reflectance spectra of electroacoustic waves for the structures “++” (Fig.
7) and “+–” (Fig. 8) reveals several main differences. The first difference between the two
reflectance spectra manifests itself in the range of the wave number k = 0, i.e., for an infinite
wavelength. At k → 0, the reflectance tends to zero for the structure “++” and to the
reflectance for a single domain wall for the structure “+–” [Shevyakhov, 1990]. Physically,
this difference in the behavior of the spectra can be explained as follows. The shear wave
Electroacoustic Waves in a Ferroelectric Crystal with of a Moving System of Domain Walls

Fig. 9. Dependences of the magnitude of the reflectance ⎜R⎜ on the angle of incidence θ'' for
the structure “++” consisting of nine domains (N = 4) in the case of k’’ = 31941 sm
-1
at the
velocities V
D
= (dashed line) 0, (thin line) 0.1v, and (thick line) –0.1v

0 20 40 60 80
0
0.2
0.4
0.6
0.8
1
|R|
θ , deg
θ
∗

Fig. 10. Dependences of the magnitude of the reflectance ⎜R⎜on the angle of incidence θ'' for
the structure “++” consisting of five domains (N = 2) in the case of k'' = 55000 cm–1 at the
velocities V
D
= (dashed line) 0, (thin line) 0.1v, and (thick line) –0.1v
Electroacoustic Waves in a Ferroelectric Crystal with of a Moving System of Domain Walls

323
with the wavelength considerably larger than 2Nd + d is “insensitive” to the structure “++,”
and the electroacoustic wave propagates in the ferroelectric as in a single-domain sample in
which the reflection is absent; i.e. ⎜R⎜ → 0 at k → 0 (Fig. 7). For the electroacoustic wave with
the wavelength λ → ∞, the structure “+–” is represented as a single domain wall, which is
confirmed by the results of numerical calculations (Fig. 8).
The second difference lies in the fact that, at the center of the allowed band, the reflectance
spectrum for the structure “++” is characterized by ⎜R⎜ = 0, whereas the reflectance
spectrum for the structure “+–” always contains the secondary maximum. Finally, the third
evident difference manifests itself in the number of peaks (the main peak plus secondary
peaks) in one band gap: their number is always odd for the structure “++” and always even
for the structure “+–.”
The dependences of the magnitude of the reflectance ⎜R⎜ of electroacoustic waves on the
angel of incidence θ'' of the electroacoustic wave on the lattice for the structure “++” are
plotted in Figs. 9 and 10. It can be seen from Fig. 9 that, for the wave number corresponding
to the center of the first band gap, it is possible to choose the condition providing an almost
total reflection (| | 1 R ≈ ) in the range of small angles of incidence. The domain-wall motion
leads to the fact that the reflectance peaks shift to